organisation europÉenne pour la recherche ......34 report handbook of lhc higgs cross sections: 1....

CERN–2012–xxx1 November 2011

ORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRE

CERN EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Handbook of LHC Higgs cross sections:

2. Differential Distributions

Report of the LHC Higgs Cross Section Working Group

Editors: S. DittmaierC. MariottiG. PassarinoR. Tanaka

GENEVA2012

1

Draft version 1.02

November 18, 2011 – 11 : 26 DRAFT ii

Conveners

Gluon-Fusion process:M. Grazzini, F. Petriello, J. Qian, F. Stöckli3

Vector-Boson-Fusion process:A. Denner, S. Farrington, C. Hackstein, C. Oleari, D. Rebuzzi4

WH/ZH production mode: S. Dittmaier, R. Harlander, C. Matteuzzi, J. Olsen, G. Piacquadio5

ttH process: C. Neu, C. Potter, L. Reina, M. Spira6

MSSM neutral Higgs:M. Spira, M. Vazquez Acosta, M. Warsinsky, G. Weiglein7

MSSM charged Higgs:M. Flechl, S. Heinemeyer, M. Krämer, S. Lehti8

PDF: S. Forte, J. Huston, K. Mazumdar, R. Thorne9

Branching ratios:A. Denner, S. Heinemeyer, I. Puljak, D. Rebuzzi10

NLO MC:M. Felcini, F. Krauss, F. Maltoni, P. Nason, J. Yu11

Higgs Pseudo-Observables:M. Dührssen, M. Felcini, G. Passarino12

γγ decay:S. Gascon-Shotkin, M. Kado13

ZZ∗ decay:N. De Filippis, S. Paganis14

WW∗ decay:J. Cuevas, T. Dai15

ττ decay:A. Nikitenko, M. Schumacher16

bb decay:C. Matteuzzi, J. Olsen, C. Potter17

H± decay:M. Flechl, S. Lehti18

ISBN ???–??–????–???-?ISSN ????–????

19

Copyright © CERN, 201120

Creative Commons Attribution 3.021

Knowledge transfer is an integral part of CERN’s mission.22

CERN publishes this report Open Access under the Creative Commons Attribution 3.0 license23

(http://creativecommons.org/licenses/by/3.0/) in order to permit its wide dissemination and24

use.25

This Report should be cited as:26

LHC Higgs Cross Section Working Group, S. Dittmaier, C. Mariotti, G. Passarino, R. Tanaka (Eds.),27

Handbook of LHC Higgs Cross Sections: 2. Differential Distributions,28

CERN-2011-??? (CERN, Geneva, 2011).29

November 18, 2011 – 11 : 26 DRAFT iii

Abstract30

This Report summarizes the results of the second years’ activities of the LHC Higgs Cross Section31

Working Group. The main goal of the working group was to present the state of the art of Higgs Physics32

at the LHC, integrating all new results that have appeared inthe last few years. The first working group33

report Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002) focuses34

on predictions (central values and errors) for total Higgs production cross sections and Higgs branching35

ratios in the Standard Model and its minimal supersymmetricextension, covering also related issues such36

as Monte Carlo generators, parton distribution functions,and pseudo-observables. This second Report37

represents the next natural step towards realistic predictions upon providing results on cross sections38

with benchmark cuts, differential distributions, detailsof specific decay channels, and further recent39

developments.40

November 18, 2011 – 11 : 26 DRAFT iv

We, the authors, would like to dedicate this Report to the memory of41

Robert Brout and Simon van der Meer.42

November 18, 2011 – 11 : 26 DRAFT v

S. Dittmaier1, C. Mariotti2, G. Passarino2,3 and R. Tanaka4 (eds.);43

...44

November 18, 2011 – 11 : 26 DRAFT vi

Prologue45

The implementation of spontaneous symmetry breaking in theframework of gauge theories in the 1960s46

triggered the breakthrough in the construction of the standard electroweak theory, as it still persists today.47

The idea of driving the spontaneous breakdown of a gauge symmetry by a self-interacting scalar field,48

which thereby lends mass to gauge bosons, is known as theHiggs mechanismand goes back to the early49

work of Refs. [1–5]. The postulate of a new scalar neutral boson, known as theHiggs particle, comes50

as a phenomenological imprint of this mechanism. Since the birth of this idea, the Higgs boson has51

successfully escaped detection in spite of tremendous search activities at the high-energy colliders LEP52

and Tevatron, leaving open the crucial question whether theHiggs mechanism is just a theoretical idea or53

a ‘true model’ for electroweak symmetry breaking. The experiments at the Large Hadron Collider (LHC)54

will answer this question, either positively upon detecting the Higgs boson, or negatively by ruling out55

the existence of a particle with properties attributed to the Higgs boson within the Standard Model. In56

this sense the outcome of the Higgs search at the LHC will either carve our present understanding of57

electroweak interactions in stone or will be the beginning of a theoretical revolution.58

November 18, 2011 – 11 : 26 DRAFT vii

59

November 18, 2011 – 11 : 26 DRAFT viii

Contents60

1 Introduction1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

2 Branching Ratios2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

2.1 SM Higgs branching ratios with uncertainties . . . . . . . . .. . . . . . . . . . . . . . 463

2.2 MSSM Higgs branching ratios . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3364

3 Parton Distribution Functions3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3565

3.1 PDF Set Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 3566

3.2 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 3567

3.3 Results for the correlation study . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 3768

3.4 Additional correlation studies . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 3969

4 NLO Parton Shower4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4570

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 4571

4.2 Uncertainties in NLO+PS results . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 4572

4.3 Uncertainties ingg → H → WW(∗) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5073

5 The Gluon-Fusion Process5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5974

5.1 Finite quark mass effects in the SM gluon fusion process in POWHEG . . . . . . . . . . . 6075

5.2 Perturbative uncertainties in exclusive jet bins . . . . .. . . . . . . . . . . . . . . . . . 6476

5.3 Perturbative uncertainties in jet-veto efficiencies . .. . . . . . . . . . . . . . . . . . . . 7077

5.4 The HiggsqT spectrum and its uncertainties . . . . . . . . . . . . . . . . . . . . . . . .7378

5.5 Monte Carlo and resummation for exclusive jet bins . . . . .. . . . . . . . . . . . . . . 7779

6 VBF production mode6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8480

6.1 Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 8481

6.2 VBF parameters and cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 8682

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 8683

7 WH/ZH production mode7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9484

7.1 Theoretical developments . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 9485

7.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 9486

8 ttH Process8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10187

8.1 NLO distributions forttH associated production . . . . . . . . . . . . . . . . . . . . . . 10188

8.2 Interface of NLOttH calculation with parton-shower Monte Carlo programs . . . . .. 10289

8.3 Thepp → ttbb background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10290

1S. Dittmaier, C. Mariotti, G. Passarino and R. Tanaka2A. Denner, S. Heinemeyer, I. Puljak, D. Rebuzzi (eds.); S. Dittmaier, A. Mück, M. Spira, M.M. Weber, G. Weiglein . . .3S. Forte, J. Huston and R. S. Thorne (eds); S. Alekhin, J. Blümlein, A.M. Cooper-Sarkar, S. Glazov, P. Jimenez-Delgado,

S. Moch, P. Nadolsky, V. Radescu, J. Rojo, A. Sapronov, W.J. Stirling.4M. Felcini, F. Krauss, F. Maltoni, P. Nason and J. Yu.5M. Grazzini, F. Petriello, J. Qian, F. Stoeckli (eds.); E.A.Bagnaschi, A. Banfi, D. de Florian, G. Degrassi, G. Ferrera,

G. Salam, P. Slavich, I. Stewart, F. Tackmann, D. Tommasini,A. Vicini, W. Waalewijn, G. Zanderighi6A. Denner, S. Farrington, C. Hackstein, C. Oleari, D. Rebuzzi (eds.); S. Dittmaier, A. Mück, S. Palmer, B. Quayle7S. Dittmaier, R.V. Harlander, J. Olsen, G. Piacquadio (eds.); A. Denner, G. Ferrera, M. Grazzini, S. Kallweit, A. Mück,

F. Tramontano.8C. Collins-Tooth, C. Neu, C. Potter, L. Reina, M. Spira (eds.); G. Bevilacqua, A. Bredenstein, M. Czakon, S. Dawson,

A. Denner, S. Dittmaier, R. Frederix, S. Frixione, M. V. Garzelli, V. Hirschi, S. Hoeche, A. Kardos, M. Krämer, F. Krauss,F. Maltoni, C. G. Papadopoulos, R. Pittau, S. Pozzorini, S. Schumann, P. Torrielli, Z. Trócsányi, D. Wackeroth, M. Worek, ....

November 18, 2011 – 11 : 26 DRAFT ix

9 γγ production mode9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10491

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 10492

9.2 Sets of Acceptance Criteria used . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 10493

9.3 Signal and background modelling . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 10494

9.4 Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 10495

9.5 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 10496

10 WW∗ decay mode10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10597

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 10598

10.2 WW background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 10599

10.3 Extrapolation parametersα. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105100

10.4 Cross section and acceptance. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 105101

10.5 Theoretical errors on acceptances. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 106102

10.6 PDF errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 107103

11 ZZ production mode11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108104

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 108105

11.2 Leading order and next to leading order generators . . . .. . . . . . . . . . . . . . . . . 108106

11.3 Higher orders Higgs transverse momentum spectrum . . . .. . . . . . . . . . . . . . . 108107

11.4 TheZZ background process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111108

12 Higgs boson production in the MSSM12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 123109

12.1 The MSSM Higgs sector: general features . . . . . . . . . . . . .. . . . . . . . . . . . 123110

12.2 Status of inclusive calculations . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 124111

12.3 Status of differential cross sections . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 129112

13 Charged Higgs boson production13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148113

13.1 Light charged Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 148114

13.2 Heavy charged Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 150115

14 Predictions for Higgs production and decay with a 4th SM-like fermion generation . . . . . 154116

14.1 General setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 154117

14.2 Higgs production via gluon fusion . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 154118

14.3 NLO corrections toH → 4f in SM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158119

14.4 H → f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158120

14.5 H → gg, γγ, γZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159121

14.6 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 160122

15 The (heavy) Higgs boson lineshape . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 169123

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 169124

15.2 Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 170125

15.3 Production and decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 173126

9S. Gascon-Shotkin, M. Kado (eds.) and ; ...10B. Di Micco, R. Di Nardo, A. Farilla, B. Mellado, F. Petrucci and (eds.); ...11N. De Filippis, S. Paganis (eds.) and S. Bolognesi, T. Cheng,K. Ellis, N. Kauer, C. Mariotti, P. Nason, I. Puljak,...12M. Spira, M. Vazquez Acosta, M. Warsinsky, G. Weiglein (eds.); E.A. Bagnashci, M. Cutajar, G. Degrassi, S. Dittmaier,

R. Harlander, S. Heinemeyer, M. Krämer, A. Nikitenko, S. Palmer, P. Slavich, A. Vicini, M. Wiesemann . . .13M. Flechl, S. Heinemeyer, M. Krämer, S. Lehti (eds.); M. Hauru, M. Spira

November 18, 2011 – 11 : 26 DRAFT x

15.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 178127

15.5 QCD scale error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 184128

15.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 185129

November 18, 2011 – 11 : 26 DRAFT 1

1 Introduction 1130

After the start ofpp collisions at the LHC the natural question is: Why precisionHiggs physics now?131

The LHC successfully started at the end of 2009 colliding twoproton beams at centre-of-mass energies132

of√s = 0.9 TeV and2.36 TeV. In 2010 the energy has been raised up to7 TeV.133

By the end of the7 TeV run in 2011 and (likely at8 TeV) in 2012 each experiment aims to collect134

an integrated luminosity of a few inverse femtobarns. Then along shutdown will allow the implemen-135

tation of necessary modifications to the machine, to restartagain at the design energy of14 TeV. By136

the end of the life of the LHC, each experiment will have collected3000 fb−1on tape. The luminos-137

ity that the experiments expect to collect with the7 TeV run will allow us to probe a wide range of138

the Higgs-boson mass. Projections of ATLAS and CMS when combining only the three main chan-139

nels (H → γγ,H → ZZ,H → WW), indicate that in case of no observed excess, the Standard Model140

(SM) Higgs boson can be excluded in the range between140 GeV and200 GeV. A 5σ significance can141

be reached for a Higgs-boson mass range between160 GeV and170 GeV. The experiments (ATLAS,142

CMS, and LHCb) are now analysing more channels in order to increase their potential for exclusion at143

lower and higher masses. For these reasons an update of the discussion of the proper definition of the144

Higgs-boson mass and width has become necessary. Indeed, inthis scenario, it is of utmost importance145

to access the best theory predictions for the Higgs cross sections and branching ratios, using definitions146

of the Higgs-boson properties that are objective functionsof the experimental data while respecting first147

principles of quantum field theory. In all parts we have triedto give a widely homogeneous summary for148

the precision observables. Comparisons among the various groups of authors are documented reflecting149

the status of our theoretical knowledge. This may be understood as providing a common opinion about150

the present situation in the calculation of Higgs cross sections and their theoretical and parametric errors.151

The experiments have a coherent plan for using the input suggestions of the theoretical community152

to facilitate the combination of the individual results. Looking for precision tests of theoretical models153

at the level of their quantum structure requires the higheststandards on the theoretical side as well.154

Therefore, this Report is the result of a workshop started asan appeal by experimentalists. Its progress155

over the subsequent months to its final form was possible onlybecause of a close contact between the156

experimental and theory communities.157

The major sections of this Report are devoted to discussing the computation of cross sections and158

branching ratios for the SM Higgs and for the Minimal Supersymmetric Standard Model (MSSM) Higgs159

bosons, including the still-remaining theoretical uncertainties. The idea of presenting updated calcula-160

tions on Higgs physics was triggered by experimentalists and is substantiated as far as possible in this161

Report. The working group was organized in10 subgroups. The first four address different Higgs pro-162

duction modes: gluon–gluon fusion, vector-boson fusion, Higgs-strahlung, and associated production163

with top-quark pairs. Two more groups are focusing on MSSM neutral and MSSM charged Higgs pro-164

duction. One group is dedicated to the prediction of the branching ratios (BR) of Higgs bosons in the SM165

and MSSM. Another group studies predictions from differentMonte Carlo (MC) codes at next-to-leading166

order (NLO) and their matching to parton-shower MCs. The definition of Higgs pseudo-observables is167

also a relevant part of this analysis, in order to correctly match the experimental observables and the the-168

oretical definitions of physical quantities. Finally, a group is devoted to parton density functions (PDFs),169

in particular to the issue of new theoretical input related to PDFs, in order to pin down the theoretical170

uncertainty on cross sections.171

To discover or exclude certain Higgs-boson mass regions different inputs are needed:172

– SM cross sections and BR in order to produce predictions;173

– theoretical uncertainties on these quantities. These uncertainties enter also the determination of174

systematic errors of the mean value.175

1S. Dittmaier, C. Mariotti, G. Passarino and R. Tanaka

November 18, 2011 – 11 : 26 DRAFT 2

Furthermore, common and correlated theoretical inputs (cross sections, PDFs, SM and MSSM176

parameters, etc.) require the highest standards on the theoretical side. The goal has been to give precise177

common inputs to the experiments to facilitate the combination of multiple Higgs search channels.178

The structure of this Report centres on a description of cross sections computed at next-to-next-179

to-leading order (NNLO) or NLO, for each of the production modes. Comparisons among the various180

groups of authors for the central value and the range of uncertainty are documented and reflect the status181

of our theoretical knowledge. Note that all the central values have been computed using the same SM182

parameters input, as presented in table Table 1 of the Appendix. An update of the previous discussions183

of theoretical uncertainties has become necessary for several reasons:184

– The PDF uncertainty has been computed following the PDF4LHC prescription as described in185

Section??of this Report.186

– Theαs uncertainty has been added in quadrature to the PDF variation.187

– The renormalization and factorization QCD scales have been varied following the criterion of188

pinning down, as much as possible, the theoretical uncertainty. It often remains the largest of the189

uncertainties.190

A final major point is that, for this Report, all cross sections have been computed within an inclusive191

setup, not taking into account the experimental cuts and theacceptance of the apparatus. A dedicated192

study of these effects (cuts on the cross sections and onK-factors) will be presented in a future publica-193

tion.194

The final part of this Report is devoted to describing a new direction of work: what the experiments195

observe in the final state is not always directly connected toa well defined theoretical quantity. We have196

to take into account the acceptance of the detector, the definition of signal, the interferencesignal–197

background, and all sorts of approximations built into the Monte Carlo codes. As an example at LEP,198

the line shape of theZ for the final state with two electrons has to be extracted fromthe cross section of199

the process (e+e− → e+e−), after having subtracted the contribution of the photon and the interference200

between the photon and theZ. A corrected definition of the Higgs-boson mass and width is needed.201

Both are connected to the corresponding complex pole in thep2 plane of the propagator with momentum202

transferp. We claim that the correct definition of mass of an unstable particle has to be used in Monte203

Carlo generators.204

Different Monte Carlo generators exist at LO and NLO. It was important to compare their predic-205

tions and to stress the corresponding differences, also taking into account the different algorithms used206

for parton shower. Note that NLO matrix-element generatorsmatched with a parton shower are the tools207

for the future. Beyond the goals of this Report remains the agreement between NLO MC predictions and208

NNLO calculations within the acceptance of the detectors. The next step in the activities of this working209

group will be the computation of cross sections that includeacceptance cuts and differential distribu-210

tions for all final states that will be considered in the Higgssearch at the LHC. Preferably this should be211

carried out with the same set of (benchmark) cuts for ATLAS and CMS. The goal is to understand how212

theK-factors from (N)LO to (N)NLO will change after introduction of cuts and to compare the NNLO213

differential distributions with the ones from Monte Carlo generators at NLO. There is a final comment214

concerning the SM background: we plan to estimate theoretical predictions for the most important back-215

grounds in the signal regions. This means that abackground control regionhas to be defined, and there216

the experiments will measure a given source of background directly from data. Thecontrol regioncan217

be in the bulk of the background production phase space, but can also be in the tail of the distributions.218

Thus it is important to define the precision with which the SM background will be measured and the219

theoretical precision available for that particular region. Then the background uncertainty should be ex-220

trapolated back to thesignal region, using available theoretical predictions and their uncertainty. It will221

be important to compute the interference between signal andbackground and try to access this at NLO.222

November 18, 2011 – 11 : 26 DRAFT 3

The (N)LO Monte Carlos will be used to simulate this background and determine how theK-factor is223

changing with the chosen kinematic cuts.224

The present documentation is the result of a workshop that started in January 2010 as a new joint225

effort for Higgs cross sections between ATLAS, CMS, and the theory community.226

In this Report the Higgs-boson cross section calculations are presented at the energy of the first227

pp run,7 TeV, as well as at the nominal one (14 TeV). Updated tables at the future energy will be made228

available at the twiki page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CrossSections .229

November 18, 2011 – 11 : 26 DRAFT 4

2 Branching Ratios 2230

For a correct interpretation of experimental data precise calculations not only of the various production231

cross sections, but also for the relevant decay widths are essential, including their respective uncertainties.232

Concerning the SM Higgs boson in Ref. [6] a first precise estimate of the branching ratios was presented.233

In Sect. 2.1 we update this prediction and supplement it withan estimate of the various uncertainties. For234

the lightest Higgs boson in the MSSM in Ref. [6] preliminary results forBR(H → τ+τ−) (φ = h,H,A)235

were given. In Sect. 2.2 we present a prediction for all relevant decay channels evaluated in themmaxh236

scenario [7].237

2.1 SM Higgs branching ratios with uncertainties238

In this section we present an update of the BR calculation as well as results for the uncertainties of the239

decay widths and BRs for a SM Higgs boson. Neglecting these uncertainties would yield in the case of240

negative search results too large excluded regions of the parameter space. In case of a Higgs-boson signal241

these uncertainties are crucial to perform a reliable and accurate determination ofMH and the Higgs-242

boson couplings [8–10]. The uncertainties arise from two sources, the missing higher-order corrections243

yield the “theoretical” uncertainties, while the experimental errors on the SM input parameters, such as244

the quark masses or the strong coupling constant, give rise to the “parametric” uncertainties. Both types245

of uncertainty have to be taken into account and combined fora reliable estimate. We investigate all246

relevant channels for the SM Higgs boson,H → tt, H → bb, H → cc, H → τ+τ−, H → µ+µ−,247

H → gg, H → γγ, H → Zγ, H → WW andH → ZZ (including detailed results also for the various248

four-fermion final states). We present results for the totalwidth, ΓH, as well as for various BRs. These249

results have also been published in Ref. [11].250

2.1.1 Programs and Strategy for Branching Ratio Calculations251

The branching ratios of the Higgs boson in the SM have been determined using the programs HDECAY252

[12–14] and PROPHECY4F [15–17]. In a first step, all partial widths have been calculated as accurately253

as possible. Then the branching ratios have been derived from this full set of partial widths. Since the254

widths are calculated for on-shell Higgs bosons, the results have to be used with care for a heavy Higgs255

boson (MH>∼ 500 GeV).256

– HDECAY calculates the decay widths and branching ratios ofthe Higgs boson(s) in the SM and257

the MSSM. For the SM it includes all kinematically allowed channels and all relevant higher-order258

QCD corrections to decays into quark pairs and into gluons. More details are given below.259

– PROPHECY4F is a Monte Carlo event generator forH → WW/ZZ → 4f (leptonic, semi-leptonic,260

and hadronic) final states. It provides the leading-order (LO) and next-to-leading-order (NLO)261

partial widths for any possible 4-fermion final state. It includes the complete NLO QCD and262

electroweak corrections and all interferences at LO and NLO. In other words, it takes into account263

both the corrections to the decays into intermediateWW andZZ states as well as their interference264

for final states that allow for both. The dominant two-loop contributions in the heavy-Higgs-mass265

limit proportional toG2µM

4H are included according to Refs. [18, 19]. Since the calculation is266

consistently performed with off-shell gauge bosons without any on-shell approximation, it is valid267

above, near, and below the gauge-boson pair thresholds. Like all other light quarks and leptons,268

bottom quarks are treated as massless. Using the LO/NLO gauge-boson widths in the LO/NLO269

calculation ensures that the effective branching ratios oftheW andZ bosons obtained by summing270

over all decay channels add up to one.271

– Electroweak next-to-leading order (NLO) corrections to the decaysH → γγ andH → gg have272

been calculated in Refs. [20–26]. They are implemented in HDECAY in form of grids based on273

2A. Denner, S. Heinemeyer, I. Puljak, D. Rebuzzi (eds.); S. Dittmaier, A. Mück, M. Spira, M.M. Weber, G. Weiglein . . .

November 18, 2011 – 11 : 26 DRAFT 5

Table 1: The SM input parameters used for the branching-ratio calculations presented in this work.

e mass 0.510998910 MeV µ mass 105.658367 MeV τ mass 1776.84 MeV

MS massmc(mc) 1.28 GeV MS massmb(mb) 4.16 GeV MS massms(2 GeV) 100 MeV

1-loop pole massmc 1.42 GeV 1-loop pole massmb 4.49 GeV pole massmt 172.5 GeV

W mass 80.36951 GeV NLO ΓW 2.08856 GeV

Z mass 91.15349 GeV NLO ΓZ 2.49581 GeV

GF 1.16637×10−5 GeV−2 α(0) 1/137.0359997 αs(M2Z) 0.119

the calculations of Ref. [25,26].274

The results presented below have been obtained as follows. The Higgs total width resulting from275

HDECAY has been modified according to the prescription276

ΓH = ΓHD − ΓHDZZ − ΓHD

WW + ΓProph.4f , (1)

whereΓH is the total Higgs width,ΓHD the Higgs width obtained from HDECAY,ΓHDZZ andΓHD

WW stand277

for the partial widths toZZ andWW calculated with HDECAY, whileΓProph.4f represents the partial278

width of H → 4f calculated with PROPHECY4F. The latter can be split into the decays intoZZ, WW,279

and the interference,280

ΓProph.4f = ΓH→W∗W∗→4f + ΓH→Z∗Z∗→4f + ΓWW/ZZ−int. . (2)

2.1.2 The SM Input-Parameter Set281

The production cross sections and decay branching ratios ofthe Higgs bosons depend on a large number282

of SM parameters. For our calculations, the input parameterset as defined in Appendix A of Ref. [6] has283

been used. The chosen values are summarized in Table 1.284

The gauge-boson masses given in Table 1 are the pole masses derived from the PDG valuesMZ =285

91.1876 GeV,ΓZ = 2.4952 GeV,MW = 80.398 GeV,ΓW = 2.141 GeV and the gauge-boson widths286

in Table 1 are calculated at NLO from the other input parameters.287

It should be noted that for our numerical analysis we have used the one-loop pole masses for288

the charm and bottom quarks and their uncertainties, since these values do not exhibit a significant289

dependence on the value of the strong coupling constantαs in contrast to theMS masses [27].290

2.1.3 Procedure for determining Uncertainties291

We included two types of uncertainty, parametric uncertainties (PU), which originate from uncertainties292

in input parameters, and theoretical uncertainties (TU), which arise from unknown contributions to the293

theoretical predictions, typically missing higher orders. Here we describe the way these uncertainties294

have been determined.295

2.1.3.1 Parametric uncertainties296

In order to determine the parametric uncertainties of the Higgs-decay branching ratios we took into297

account the uncertainties of the input parametersαs,mc,mb, andmt. The considered variation of these298

input parameters is given in Table 2. The variation inαs corresponds to three times the error given in299

Refs. [28, 29]. The uncertainties formb andmc are a compromise between the errors of Ref. [29] and300

the errors from the most precise evaluations [30–32]. Formc our error corresponds roughly to the one301

November 18, 2011 – 11 : 26 DRAFT 6

Table 2: Input parameters and their relative uncertainties, as usedfor the uncertainty estimation of the branchingratios. The masses of the central values correspond to the 1-loop pole masses, while the last column contains thecorrespondingMS mass values.

Parameter Central Value Uncertainty MS massesmq(mq)

αs(MZ) 0.119 ±0.002

mc 1.42 GeV ±0.03 GeV 1.28 GeV

mb 4.49 GeV ±0.06 GeV 4.16 GeV

mt 172.5 GeV ±2.5 GeV 165.4 GeV

obtained in Ref. [33]. Finally, the assumed error formt is about twice the error from the most recent302

combination of CDF and DØ [34].303

We did not consider parametric uncertainties resulting from experimental errors onGF ,MZ,MW304

and the lepton masses, because their impact is below one per mille. We also did not include uncertainties305

for the light quarks u, d, s as the corresponding branching ratios are very small and the impact on306

other branching ratios is negligible. Since we usedGF to fix the electromagnetic couplingα(MZ),307

uncertainties in the hadronic vacuum polarisation do not matter.308

Given the uncertainties in the parameters, the parametric uncertainties have been determined as309

follows. For each parameterp = αs,mc,mb,mt we have calculated the Higgs branching ratios forp,310

p +∆p andp −∆p, while all other parameters have been left at their central values. The error on each311

branching ratio has then been determined by312

∆p+BR = max{BR(p +∆p),BR(p),BR(p−∆p)} − BR(p)

∆p−BR = BR(p)−min{BR(p +∆p),BR(p),BR(p −∆p)}. (3)

The total parametric errors have been obtained by adding theparametric errors from the four parameter313

variations in quadrature. This procedure ensures that the branching ratios add up to unity for all parameter314

variations individually.315

The uncertainties of the partial and total decay widths havebeen obtained in an analogous way,316

∆p+Γ = max{Γ(p +∆p),Γ(p),Γ(p −∆p)} − Γ(p)

∆p−Γ = Γ(p)−min{Γ(p+∆p),Γ(p),Γ(p −∆p)}. (4)

whereΓ denotes the partial decay width for each considered decay channel or the total width, respec-317

tively. The total parametric errors have been derived by adding the individual parametric errors in quadra-318

ture.319

2.1.3.2 Theoretical uncertainties320

The second type of uncertainty for the Higgs branching ratios results from approximations in the theoret-321

ical calculations, the dominant effects being due to missing higher orders. Since the decay widths have322

been calculated with HDECAY and PROPHECY4F the missing contributions in these codes are relevant.323

For QCD corrections the uncertainties have been estimated by the scale dependence of the widths result-324

ing from a variation of the scale up and down by a factor 2 or from the size of known omitted corrections.325

For electroweak corrections the missing higher orders havebeen estimated based on the known struc-326

ture and size of the NLO corrections. For cases where HDECAY takes into account the known NLO327

corrections only approximatively the accuracy of these approximations has been used. The estimated328

relative theoretical uncertainties for the partial widthsresulting from missing higher-order corrections329

are summarized in Table 3. The corresponding uncertainty for the total width is obtained by adding the330

uncertainties for the partial widths linearly.331

November 18, 2011 – 11 : 26 DRAFT 7

Table 3: Estimated theoretical uncertainties from missing higher orders.

Partial Width QCD Electroweak Total

H → bb/cc ∼ 0.1% ∼ 1–2% for MH<∼ 135 GeV ∼ 2%

H → τ+τ−/µ+µ− ∼ 1–2% for MH<∼ 135 GeV ∼ 2%

H → tt <∼ 5% <∼ 2–5% for MH < 500 GeV ∼ 5%

∼ 0.1(MH

1 TeV)4 for MH > 500 GeV ∼ 5–10%

H → gg ∼ 3% ∼ 1% ∼ 3%

H → γγ < 1% < 1% ∼ 1%

H → Zγ < 1% ∼ 5% ∼ 5%

H → WW/ZZ → 4f < 0.5% ∼ 0.5% for MH < 500 GeV ∼ 0.5%

∼ 0.17(MH

1 TeV)4 for MH > 500 GeV ∼ 0.5–15%

Specifically, the uncertainties of the partial widths calculated with HDECAY are obtained as332

follows: For the decaysH → bb, cc, HDECAY includes the complete massless QCD corrections up333

to and including NNNNLO, with a corresponding scale dependence of about0.1% [35–42]. The NLO334

electroweak corrections [43–46] are included in the approximation for small Higgs masses [47] which335

has an accuracy of about1−2% for MH < 135 GeV. The same applies to the electroweak corrections to336

H → τ+τ−. For Higgs decays into top quarks HDECAY includes the complete NLO QCD corrections337

[48–54] interpolated to the large-Higgs-mass results at NNNNLO far above the threshold [35–42]. The338

corresponding scale dependence is below5%. Only the NLO electroweak corrections due to the self-339

interaction of the Higgs boson are included, and the neglected electroweak corrections amount to about340

2−5% for MH < 500 GeV, where5% refers to the region near thett threshold and2% to Higgs341

masses far above. ForMH > 500 GeV higher-order heavy-Higgs corrections [55–60] dominate the error,342

resulting in an uncertainty of about0.1 × (MH/1 TeV)4 for MH > 500 GeV. ForH → gg, HDECAY343

uses the NLO [61–63], NNLO [64], and NNNLO [65] QCD corrections in the limit of heavy top quarks.344

The uncertainty from the scale dependence at NNNLO is about3%. The NLO electroweak corrections345

are included via an interpolation based on a grid from Ref. [26]; the uncertainty from missing higher-346

order electroweak corrections is estimated to be1%. For the decayH → γγ, HDECAY includes the full347

NLO QCD corrections [63, 66–71] and a grid from Ref. [25, 26] for the NLO electroweak corrections.348

Missing higher orders are estimated to be below1%. The contribution of theH → γe+e− decay via349

virtual photon conversion, evaluated in Ref. [72] is not taken into account in the following results. Its350

correct treatment and its inclusion in HDECAY are in progress.3 The partial decay widthH → Zγ is351

included in HDECAYat LO including the virtualW , top, bottom andτ loop contributions. The QCD352

corrections are small in the intermediate-Higgs-mass range [73] and can thus safely be neglected. The353

associated theoretical uncertainty ranges at the level below one per cent. The electroweak corrections to354

this decay mode are unknown and thus imply a theoretical uncertainty of about 5% in the intermediate-355

Higgs-mass range.356

The decaysH → WW/ZZ → 4f are based on PROPHECY4F, which includes the complete NLO357

QCD and electroweak corrections with all interferences andleading two-loop heavy-Higgs corrections.358

For small Higgs-boson masses the missing higher-order corrections are estimated to roughly0.5%. For359

MH > 500 GeV higher-order heavy-Higgs corrections dominate the error leading to an uncertainty of360

about0.17 × (MH/1 TeV)4.361

Based on the error estimates for the partial widths in Table 3, the theoretical uncertainties for the362

3The contribution ofH → γe+e− is part of the QED corrections toH → γγ which are expected to be small in total.

November 18, 2011 – 11 : 26 DRAFT 8

[GeV]HM100 120 140 160 180 200

Hig

gs B

R +

Tot

al U

ncer

t

-310

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

bb

ττ

cc

gg

γγ γZ

WW

ZZ

Fig. 1: Higgs branching ratios and their uncertainties for the low mass range.

branching ratios are determined as follows. For the partialwidthsH → bb, cc, τ+τ−, gg, γγ the total363

uncertainty given in Table 3 is used. ForH → tt andH → WW/ZZ → 4f , the total uncertainty is364

used forMH < 500 GeV, while for higher Higgs masses the QCD and electroweak uncertainties are365

added linearly. Then the shifts of all branching ratios are calculated resulting from the scaling of an366

individual partial width by the corresponding relative error (since each branching ratio depends on all367

partial widths, scaling a single partial width modifies all branching ratios). This is done by scaling each368

partial width separately while fixing all others to their central values, resulting in individual theoretical369

uncertainties of each branching ratio. However, since the errors for allH → WW/ZZ → 4f decays370

are correlated forMH > 500 GeV or small below, we only consider the simultaneous scaling of all371

4-fermion partial widths. The thus obtained individual theoretical uncertainties for the branching ratios372

are combined linearly to obtain the total theoretical uncertainties.373

Finally, the total uncertainties are obtained by adding linearly the total parametric uncertainties374

and the total theoretical uncertainties.375

2.1.4 Results376

In this Section the results of the SM Higgs branching ratios,calculated according to the procedure de-377

scribed above, are shown and discussed. Figure 1 shows the SMHiggs branching ratios in the low378

mass range,100 GeV ≤ MH ≤ 200 GeV as solid lines. The (coloured) bands around the lines379

show the respective uncertainties, estimated consideringboth the theoretical and the parametric uncer-380

tainty sources (as discussed in Section 2.1.3). The same results, but now for the “full” mass range,381

100 GeV ≤ MH ≤ 1000 GeV, are shown in Figure 2. More detailed results on the decays H → WW382

andH → ZZ with the subsequent decay to4f are presented in Figures 3 and 4. The largest “visible”383

uncertainties are found for the channelsH → τ+τ−, H → gg, H → cc andH → tt, see below.384

In the following we list the branching ratios for the Higgs two-body fermionic and bosonic final385

November 18, 2011 – 11 : 26 DRAFT 9

[GeV]HM100 200 300 400 500 1000

Hig

gs B

R +

Tot

al U

ncer

t

-310

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

bb

ττ

cc

ttgg

γγ γZ

WW

ZZ

Fig. 2: Higgs branching ratios and their uncertainties for the fullmass range.

[GeV]HM100 200 300 400 500 1000

Hig

gs B

R +

Tot

al U

ncer

t

-510

-410

-310

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

τ,µllll, l=e,

µllll, l=e,

eeeeµµee

=anyν, τ,µ, l=e,ννll=anyν, µ, l=e,ννll

ν eνeν µ νe

Fig. 3: Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their uncertainties for thefull mass range.

November 18, 2011 – 11 : 26 DRAFT 10

[GeV]HM100 200 300 400 500 1000

Hig

gs B

R +

Tot

al U

ncer

t

-310

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

, q=udcsbτ,µllqq, l=e,, q=udcsbµllqq, l=e,

=any, q=udcsbνqq, νν

, q=udcsbµqq, l=e,νl

qqqq, q=udcsb

ffff, f=any fermion

Fig. 4: Higgs branching ratios forH → 4q, H → 4f andH → 2q2l, 2qlν, 2q2ν final states and their uncertaintiesfor the full mass range.

states, together with their uncertainties, estimated as discussed in Section 2.1.3. Detailed results for four386

representative Higgs-boson masses are given in Table 4. Here we show the BR, the PU separately for387

the four parameters as given in Table 2, the total PU, the theoretical uncertainty TU as well as the total388

uncertainty on the Higgs branching ratios. The TU are most relevant for theH → gg, H → Zγ and389

H → tt branching ratios, reachingO(10%). For theH → bb, H → cc andH → τ+τ− branching390

ratios they remain below a few percent. PU are relevant mostly for theH → cc andH → gg branching391

ratios, reaching up toO(10%) andO(5%), respectively. They are mainly induced by the parametric392

uncertainties inαs andmc. The PU resulting frommb affect theBR(H → bb) at the level of3%,393

and the PU frommt influences in particular theBR(H → tt) near thett threshold. For theH → γγ394

channel the total uncertainty can reach up to about5% in the relevant mass range. Both TU and PU on395

the important channelsH → ZZ andH → WW remain at the level of 1% over the full mass range,396

giving rise to a total uncertainty below 3% forMH > 135 GeV. In Tables 5–14 we list the branching397

ratios for the Higgs two-body fermionic and bosonic final states, together with their total uncertainties,398

for various Higgs-boson masses.4 Tables 10–14 also contain the total Higgs widthΓH in the last column.399

Finally, Tables 15–19 and Tables 20–24, list the branching ratios for the most relevant Higgs de-400

cays into four-fermion final states. The right column in these Tables shows the total relative uncertainties401

on these branching ratios in percentage. These are practically equal for all theH → 4f branching ratios402

and the same as those forH → WW/ZZ. It should be noted that the charge-conjugate state is not403

included forH → lνqq.404

We would like to remark that, when possible, the branching ratios for Higgs into four fermions,405

explicitly calculated and listed in Tables 15–24, should bepreferred to the option of calculating406

BR(H → VV)× BR(V → f f)× BR(V → f f)× (statistical factor) (5)

4The value0.0% means that the uncertainty is below0.05%.

November 18, 2011 – 11 : 26 DRAFT 11

Table 4: SM Higgs branching ratios and their relative parametric (PU), theoretical (TU) and total uncertainties fora selection of Higgs masses. For PU, all the single contributions are shown. For these four columns, the upperpercentage value (with its sign) refers to the positive variation of the parameter, while the lower one refers to thenegative variation of the parameter.

Channel MH[ GeV] BR ∆mc ∆mb ∆mt ∆αs PU TU Total

120 6.48E-01 −0.2%+0.2%

+1.1%−1.2%

+0.0%−0.0%

−1.0%+0.9%

+1.5%−1.5%

+1.3%−1.3%

+2.8%−2.8%

150 1.57E-01 −0.1%+0.1%

+2.7%−2.7%

+0.1%−0.1%

−2.2%+2.1%

+3.4%−3.5%

+0.6%−0.6%

+4.0%−4.0%

H → bb200 2.40E-03 −0.0%

+0.0%+3.2%−3.2%

+0.0%−0.1%

−2.5%+2.5%

+4.1%−4.1%

+0.5%−0.5%

+4.6%−4.6%

500 1.09E-04 −0.0%+0.0%

+3.2%−3.2%

+0.1%−0.1%

−2.8%+2.8%

+4.3%−4.3%

+3.0%−1.1%

+7.2%−5.4%

120 7.04E-02 −0.2%+0.2%

−2.0%+2.1%

+0.1%−0.1%

+1.4%−1.3%

+2.5%−2.4%

+3.6%−3.6%

+6.1%−6.0%

150 1.79E-02 −0.1%+0.1%

−0.5%+0.5%

+0.1%−0.1%

+0.3%−0.3%

+0.6%−0.6%

+2.5%−2.5%

+3.0%−3.1%

H → τ+τ−

200 2.87E-04 −0.0%+0.0%

−0.0%+0.0%

+0.0%−0.1%

+0.0%−0.0%

+0.0%−0.1%

+2.5%−2.5%

+2.5%−2.6%

500 1.53E-05 −0.0%+0.0%

−0.0%+0.0%

+0.1%−0.1%

−0.1%+0.0%

+0.1%−0.1%

+5.0%−3.1%

+5.0%−3.2%

120 2.44E-04 −0.2%+0.2%

−2.0%+2.1%

+0.1%−0.1%

+1.4%−1.3%

+2.5%−2.5%

+3.9%−3.9%

+6.4%−6.3%

150 6.19E-05 −0.0%+0.0%

−0.5%+0.5%

+0.1%−0.1%

+0.3%−0.3%

+0.6%−0.6%

+2.5%−2.5%

+3.1%−3.2%

H → µ+µ−

200 9.96E-07 −0.0%−0.0%

−0.0%+0.0%

+0.1%−0.1%

+0.0%−0.0%

+0.1%−0.1%

+2.5%−2.5%

+2.6%−2.6%

500 5.31E-08 −0.0%+0.0%

−0.0%+0.0%

+0.1%−0.1%

−0.0%+0.0%

+0.1%−0.1%

+5.0%−3.1%

+5.1%−3.1%

120 3.27E-02 +6.0%−5.8%

−2.1%+2.2%

+0.1%−0.1%

−5.8%+5.6%

+8.5%−8.5%

+3.8%−3.7%

+12.2%−12.2%

150 7.93E-03 +6.2%−6.0%

−0.6%+0.6%

+0.1%−0.1%

−6.9%+6.8%

+9.2%−9.2%

+0.6%−0.6%

+9.7%−9.7%H → cc

200 1.21E-04 +6.2%−6.1%

−0.2%+0.1%

+0.1%−0.2%

−7.2%+7.2%

+9.5%−9.5%

+0.5%−0.5%

+10.0%−10.0%

500 5.47E-06 +6.2%−6.0%

−0.1%+0.1%

+0.1%−0.1%

−7.6%+7.6%

+9.8%−9.7%

+3.0%−1.1%

+12.8%−10.7%

350 1.56E-02 +0.0%+0.0%

−0.0%+0.0%

−78.6%+120.9%

+0.9%−0.9%

+120.9%−78.6%

+6.9%−12.7%

+127.8%−91.3%

360 5.14E-02 −0.0%−0.0%

−0.0%+0.0%

−36.2%+35.6%

+0.7%−0.7%

+35.6%−36.2%

+6.6%−12.2%

+42.2%−48.4%H → tt

400 1.48E-01 +0.0%+0.0%

−0.0%+0.0%

−6.8%+6.2%

+0.4%−0.3%

+6.2%−6.8%

+5.9%−11.1%

+12.2%−17.8%

500 1.92E-01 −0.0%+0.0%

−0.0%+0.0%

−0.3%+0.1%

+0.1%−0.2%

+0.1%−0.3%

+4.5%−9.5%

+4.6%−9.8%

120 8.82E-02 −0.2%+0.2%

−2.2%+2.2%

−0.2%+0.2%

+5.7%−5.4%

+6.1%−5.8%

+4.5%−4.5%

+10.6%−10.3%

150 3.46E-02 −0.1%+0.1%

−0.7%+0.6%

−0.3%+0.3%

+4.4%−4.2%

+4.4%−4.3%

+3.5%−3.5%

+7.9%−7.8%H → gg

200 9.26E-04 −0.0%−0.0%

−0.1%+0.1%

−0.6%+0.6%

+3.9%−3.8%

+3.9%−3.9%

+3.7%−3.7%

+7.6%−7.6%

500 6.04E-04 −0.0%+0.0%

−0.0%+0.0%

+1.6%−1.6%

+3.4%−3.3%

+3.7%−3.7%

+6.2%−4.3%

+9.9%−7.9%

120 2.23E-03 −0.2%+0.2%

−2.0%+2.1%

+0.0%+0.0%

+1.4%−1.3%

+2.5%−2.4%

+2.9%−2.9%

+5.4%−5.3%

150 1.37E-03 +0.0%+0.1%

−0.5%+0.5%

+0.1%−0.0%

+0.3%−0.3%

+0.6%−0.6%

+1.6%−1.5%

+2.1%−2.1%H → γγ

200 5.51E-05 −0.0%−0.0%

−0.0%+0.0%

+0.1%−0.1%

+0.0%−0.0%

+0.1%−0.1%

+1.5%−1.5%

+1.6%−1.6%

500 3.12E-07 −0.0%+0.0%

−0.0%+0.0%

+8.0%−6.5%

−0.7%+0.7%

+8.0%−6.6%

+4.0%−2.1%

+11.9%−8.7%

120 1.11E-03 −0.3%+0.2%

−2.1%+2.1%

+0.0%−0.1%

+1.4%−1.4%

+2.5%−2.5%

+6.9%−6.8%

+9.4%−9.3%

150 2.31E-03 −0.1%+0.0%

−0.6%+0.5%

+0.0%−0.1%

+0.2%−0.3%

+0.5%−0.6%

+5.5%−5.5%

+6.0%−6.2%H → Zγ

200 1.75E-04 −0.0%−0.0%

−0.0%+0.0%

+0.0%−0.1%

+0.0%−0.0%

+0.0%−0.1%

+5.5%−5.5%

+5.5%−5.6%

500 7.58E-06 −0.0%+0.0%

−0.0%+0.0%

+0.8%−0.6%

−0.0%+0.0%

+0.8%−0.6%

+8.0%−6.1%

+8.7%−6.7%

120 1.41E-01 −0.2%+0.2%

−2.0%+2.1%

−0.0%+0.0%

+1.4%−1.4%

+2.5%−2.5%

+2.2%−2.2%

+4.8%−4.7%

150 6.96E-01 −0.1%+0.1%

−0.5%+0.5%

−0.0%+0.0%

+0.3%−0.3%

+0.6%−0.6%

+0.3%−0.3%

+0.9%−0.8%H → WW

200 7.41E-01 −0.0%−0.0%

−0.0%+0.0%

−0.0%+0.0%

+0.0%−0.0%

+0.0%−0.0%

+0.0%−0.0%

+0.0%−0.0%

500 5.46E-01 −0.0%+0.0%

−0.0%+0.0%

+0.1%−0.0%

−0.0%+0.0%

+0.1%−0.1%

+2.3%−1.1%

+2.4%−1.1%

120 1.59E-02 −0.2%+0.2%

−2.0%+2.1%

−0.0%+0.0%

+1.4%−1.4%

+2.5%−2.5%

+2.2%−2.2%

+4.8%−4.7%

150 8.25E-02 −0.1%+0.1%

−0.5%+0.5%

+0.0%+0.0%

+0.3%−0.3%

+0.6%−0.6%

+0.3%−0.3%

+0.9%−0.8%H → ZZ

200 2.55E-01 −0.0%+0.0%

−0.0%+0.0%

+0.0%−0.0%

+0.0%−0.0%

+0.0%−0.0%

+0.0%−0.0%

+0.0%−0.0%

500 2.61E-01 +0.0%−0.0%

−0.0%+0.0%

+0.0%+0.0%

−0.0%+0.0%

+0.1%−0.0%

+2.3%−1.1%

+2.3%−1.1%

November 18, 2011 – 11 : 26 DRAFT 12

whereV = W,Z. The formula (5) is based on narrow Higgs-width approximation and supposes theW407

andZ gauge bosons to be on shell and thus neglects, in particular,all interferences between different408

four-fermion final states. This approximation is generallynot accurate enough for Higgs masses below409

and near theWW/ZZ threshold. A study of the ratio of (5) over the PROPHECY4F prediction is reported410

and discussed inhttps://twiki.cern.ch/twiki/bin/view/LHCPhysics/BRs.411

A comparison of our results with previous calculations can be found in Ref. [11].412

November 18, 2011 – 11 : 26 DRAFT 13

Table 5: SM Higgs branching ratios to two fermions and their total uncertainties (expressed in percentage). Verylow mass range.

MH [GeV] H → bb H → τ+τ− H → µ+µ− H → cc

90.0 8.10E-01+1.6%−1.6%

8.33E-02+7.0%−6.8%

2.89E-04+7.3%−7.1%

4.10E-02+12.1%−12.1%

95.0 8.02E-01+1.7%−1.7%

8.32E-02+6.9%−6.8%

2.89E-04+7.3%−7.1%

4.05E-02+12.2%−12.1%

100.0 7.89E-01+1.8%−1.8%

8.28E-02+6.9%−6.7%

2.88E-04+7.2%−7.0%

3.99E-02+12.2%−12.2%

105.0 7.71E-01+1.9%−2.0%

8.17E-02+6.8%−6.7%

2.84E-04+7.1%−7.0%

3.90E-02+12.2%−12.2%

110.0 7.44E-01+2.1%−2.2%

7.95E-02+6.6%−6.5%

2.76E-04+7.0%−6.8%

3.75E-02+12.2%−12.2%

110.5 7.40E-01+2.1%−2.2%

7.91E-02+6.6%−6.5%

2.75E-04+6.9%−6.8%

3.74E-02+12.2%−12.2%

111.0 7.37E-01+2.2%−2.2%

7.89E-02+6.6%−6.5%

2.74E-04+6.9%−6.8%

3.72E-02+12.2%−12.2%

111.5 7.33E-01+2.2%−2.3%

7.86E-02+6.6%−6.5%

2.72E-04+6.9%−6.8%

3.70E-02+12.2%−12.2%

112.0 7.29E-01+2.2%−2.3%

7.82E-02+6.5%−6.4%

2.71E-04+6.9%−6.7%

3.68E-02+12.2%−12.2%

112.5 7.25E-01+2.3%−2.3%

7.79E-02+6.5%−6.4%

2.70E-04+6.8%−6.7%

3.66E-02+12.2%−12.2%

113.0 7.21E-01+2.3%−2.4%

7.75E-02+6.5%−6.4%

2.69E-04+6.8%−6.7%

3.64E-02+12.2%−12.2%

113.5 7.17E-01+2.3%−2.4%

7.71E-02+6.5%−6.4%

2.67E-04+6.8%−6.7%

3.62E-02+12.2%−12.2%

114.0 7.12E-01+2.4%−2.4%

7.67E-02+6.5%−6.3%

2.66E-04+6.8%−6.7%

3.59E-02+12.2%−12.2%

114.5 7.08E-01+2.4%−2.4%

7.63E-02+6.4%−6.3%

2.64E-04+6.8%−6.6%

3.57E-02+12.2%−12.2%

115.0 7.03E-01+2.4%−2.5%

7.58E-02+6.4%−6.3%

2.63E-04+6.7%−6.6%

3.55E-02+12.2%−12.2%

115.5 6.98E-01+2.4%−2.5%

7.54E-02+6.4%−6.3%

2.61E-04+6.7%−6.6%

3.52E-02+12.2%−12.2%

116.0 6.93E-01+2.5%−2.5%

7.49E-02+6.4%−6.2%

2.60E-04+6.7%−6.6%

3.50E-02+12.2%−12.2%

116.5 6.88E-01+2.5%−2.6%

7.44E-02+6.3%−6.2%

2.58E-04+6.6%−6.5%

3.48E-02+12.2%−12.2%

117.0 6.83E-01+2.5%−2.6%

7.39E-02+6.3%−6.2%

2.56E-04+6.6%−6.5%

3.44E-02+12.2%−12.2%

117.5 6.77E-01+2.6%−2.6%

7.33E-02+6.3%−6.2%

2.54E-04+6.6%−6.5%

3.42E-02+12.2%−12.2%

118.0 6.72E-01+2.6%−2.7%

7.28E-02+6.2%−6.1%

2.52E-04+6.5%−6.4%

3.40E-02+12.2%−12.2%

118.5 6.66E-01+2.6%−2.7%

7.22E-02+6.2%−6.1%

2.50E-04+6.5%−6.4%

3.37E-02+12.2%−12.2%

119.0 6.60E-01+2.7%−2.8%

7.16E-02+6.2%−6.1%

2.48E-04+6.5%−6.4%

3.33E-02+12.2%−12.2%

119.5 6.54E-01+2.7%−2.8%

7.10E-02+6.2%−6.0%

2.46E-04+6.4%−6.3%

3.31E-02+12.2%−12.2%

120.0 6.48E-01+2.8%−2.8%

7.04E-02+6.1%−6.0%

2.44E-04+6.4%−6.3%

3.27E-02+12.2%−12.2%

120.5 6.41E-01+2.8%−2.9%

6.97E-02+6.1%−6.0%

2.42E-04+6.4%−6.3%

3.24E-02+12.2%−12.2%

121.0 6.35E-01+2.9%−2.9%

6.91E-02+6.0%−5.9%

2.39E-04+6.3%−6.2%

3.21E-02+12.2%−12.2%

121.5 6.28E-01+2.9%−3.0%

6.84E-02+6.0%−5.9%

2.37E-04+6.3%−6.2%

3.17E-02+12.2%−12.2%

122.0 6.21E-01+2.9%−3.0%

6.77E-02+6.0%−5.9%

2.35E-04+6.2%−6.1%

3.14E-02+12.2%−12.2%

122.5 6.14E-01+3.0%−3.0%

6.70E-02+5.9%−5.8%

2.33E-04+6.2%−6.1%

3.10E-02+12.2%−12.2%

123.0 6.07E-01+3.0%−3.1%

6.63E-02+5.9%−5.8%

2.31E-04+6.2%−6.0%

3.07E-02+12.2%−12.2%

123.5 6.00E-01+3.1%−3.1%

6.56E-02+5.8%−5.8%

2.28E-04+6.1%−6.0%

3.03E-02+12.2%−12.2%

124.0 5.92E-01+3.1%−3.2%

6.48E-02+5.8%−5.7%

2.25E-04+6.1%−6.0%

2.99E-02+12.2%−12.2%

124.5 5.84E-01+3.2%−3.2%

6.39E-02+5.8%−5.7%

2.22E-04+6.0%−5.9%

2.95E-02+12.2%−12.2%

125.0 5.77E-01+3.2%−3.3%

6.32E-02+5.7%−5.7%

2.20E-04+6.0%−5.9%

2.91E-02+12.2%−12.2%

125.5 5.69E-01+3.3%−3.3%

6.24E-02+5.7%−5.6%

2.17E-04+6.0%−5.8%

2.87E-02+12.2%−12.2%

126.0 5.61E-01+3.3%−3.4%

6.15E-02+5.6%−5.6%

2.14E-04+5.9%−5.8%

2.83E-02+12.2%−12.2%

126.5 5.53E-01+3.4%−3.4%

6.08E-02+5.6%−5.5%

2.11E-04+5.9%−5.7%

2.79E-02+12.2%−12.2%

127.0 5.45E-01+3.4%−3.5%

5.99E-02+5.5%−5.5%

2.08E-04+5.8%−5.7%

2.75E-02+12.2%−12.2%

127.5 5.37E-01+3.5%−3.5%

5.90E-02+5.5%−5.4%

2.05E-04+5.8%−5.6%

2.71E-02+12.2%−12.2%

128.0 5.28E-01+3.5%−3.6%

5.81E-02+5.4%−5.4%

2.01E-04+5.7%−5.6%

2.67E-02+12.2%−12.2%

128.5 5.19E-01+3.6%−3.6%

5.72E-02+5.4%−5.3%

1.98E-04+5.7%−5.5%

2.63E-02+12.2%−12.2%

129.0 5.11E-01+3.6%−3.7%

5.63E-02+5.3%−5.3%

1.95E-04+5.6%−5.5%

2.58E-02+12.2%−12.2%

129.5 5.02E-01+3.7%−3.7%

5.54E-02+5.3%−5.3%

1.92E-04+5.6%−5.5%

2.54E-02+12.2%−12.2%

130.0 4.94E-01+3.7%−3.8%

5.45E-02+5.3%−5.2%

1.90E-04+5.5%−5.4%

2.49E-02+12.2%−12.1%

November 18, 2011 – 11 : 26 DRAFT 14

Table 6: SM Higgs branching ratios to two fermions and their total uncertainties (expressed in percentage). Lowand intermediate mass range.


130.5 4.85E-01+3.8%−3.8%

5.36E-02+5.2%−5.2%

1.86E-04+5.5%−5.4%

2.45E-02+12.2%−12.1%

131.0 4.76E-01+3.8%−3.9%

5.26E-02+5.2%−5.1%

1.82E-04+5.4%−5.3%

2.41E-02+12.2%−12.1%

131.5 4.67E-01+3.9%−3.9%

5.17E-02+5.1%−5.1%

1.80E-04+5.4%−5.3%

2.36E-02+12.2%−12.1%

132.0 4.58E-01+3.9%−4.0%

5.07E-02+5.1%−5.0%

1.77E-04+5.3%−5.2%

2.32E-02+12.2%−12.1%

132.5 4.49E-01+4.0%−4.0%

4.97E-02+5.0%−5.0%

1.72E-04+5.2%−5.2%

2.27E-02+12.2%−12.1%

133.0 4.40E-01+4.0%−4.1%

4.88E-02+5.0%−4.9%

1.69E-04+5.2%−5.1%

2.23E-02+12.2%−12.1%

133.5 4.31E-01+4.1%−4.2%

4.79E-02+4.9%−4.9%

1.67E-04+5.1%−5.1%

2.18E-02+12.2%−12.1%

134.0 4.22E-01+4.1%−4.2%

4.68E-02+4.8%−4.8%

1.63E-04+5.1%−5.0%

2.13E-02+12.2%−12.1%

134.5 4.13E-01+4.2%−4.3%

4.59E-02+4.8%−4.8%

1.60E-04+5.0%−5.0%

2.09E-02+12.2%−12.1%

135.0 4.04E-01+4.2%−4.3%

4.49E-02+4.8%−4.8%

1.55E-04+5.0%−4.9%

2.04E-02+12.2%−12.1%

135.5 3.95E-01+4.2%−4.2%

4.39E-02+4.6%−4.6%

1.52E-04+4.8%−4.8%

2.00E-02+11.9%−11.8%

136.0 3.86E-01+4.1%−4.1%

4.29E-02+4.5%−4.5%

1.49E-04+4.7%−4.7%

1.95E-02+11.6%−11.6%

136.5 3.77E-01+4.0%−4.0%

4.20E-02+4.4%−4.4%

1.45E-04+4.6%−4.6%

1.91E-02+11.4%−11.3%

137.0 3.68E-01+3.9%−4.0%

4.10E-02+4.3%−4.3%

1.42E-04+4.5%−4.5%

1.86E-02+11.1%−11.1%

137.5 3.59E-01+3.8%−3.9%

4.00E-02+4.2%−4.2%

1.39E-04+4.3%−4.4%

1.81E-02+10.8%−10.8%

138.0 3.50E-01+3.7%−3.8%

3.91E-02+4.1%−4.1%

1.35E-04+4.2%−4.3%

1.77E-02+10.6%−10.5%

138.5 3.41E-01+3.7%−3.7%

3.81E-02+3.9%−4.0%

1.32E-04+4.1%−4.2%

1.73E-02+10.3%−10.3%

139.0 3.32E-01+3.6%−3.6%

3.71E-02+3.8%−3.8%

1.29E-04+4.0%−4.0%

1.68E-02+10.0%−10.0%

139.5 3.23E-01+3.5%−3.5%

3.62E-02+3.7%−3.7%

1.25E-04+3.8%−3.9%

1.63E-02+9.8%−9.8%

140.0 3.15E-01+3.4%−3.4%

3.52E-02+3.6%−3.6%

1.22E-04+3.7%−3.8%

1.58E-02+9.5%−9.5%

141.0 2.97E-01+3.5%−3.5%

3.33E-02+3.5%−3.5%

1.15E-04+3.6%−3.7%

1.50E-02+9.5%−9.5%

142.0 2.81E-01+3.5%−3.5%

3.15E-02+3.5%−3.5%

1.09E-04+3.6%−3.6%

1.41E-02+9.5%−9.6%

143.0 2.64E-01+3.6%−3.6%

2.97E-02+3.4%−3.4%

1.03E-04+3.5%−3.6%

1.33E-02+9.5%−9.6%

144.0 2.48E-01+3.7%−3.6%

2.79E-02+3.4%−3.4%

9.67E-05+3.5%−3.5%

1.25E-02+9.5%−9.7%

145.0 2.32E-01+3.7%−3.7%

2.61E-02+3.3%−3.3%

9.06E-05+3.4%−3.4%

1.16E-02+9.6%−9.7%

146.0 2.16E-01+3.8%−3.8%

2.44E-02+3.3%−3.3%

8.46E-05+3.4%−3.4%

1.09E-02+9.6%−9.7%

147.0 2.01E-01+3.8%−3.8%

2.27E-02+3.2%−3.2%

7.87E-05+3.3%−3.3%

1.01E-02+9.6%−9.7%

148.0 1.85E-01+3.9%−3.9%

2.09E-02+3.1%−3.2%

7.26E-05+3.2%−3.3%

9.35E-03+9.7%−9.7%

149.0 1.72E-01+3.9%−4.0%

1.94E-02+3.1%−3.1%

6.74E-05+3.2%−3.2%

8.65E-03+9.7%−9.7%

150.0 1.57E-01+4.0%−4.0%

1.79E-02+3.0%−3.1%

6.19E-05+3.1%−3.2%

7.93E-03+9.7%−9.7%

151.0 1.43E-01+4.0%−4.1%

1.62E-02+3.0%−3.0%

5.65E-05+3.1%−3.1%

7.23E-03+9.8%−9.7%

152.0 1.30E-01+4.1%−4.1%

1.48E-02+3.0%−3.0%

5.13E-05+3.0%−3.1%

6.57E-03+9.8%−9.8%

153.0 1.17E-01+4.2%−4.2%

1.34E-02+2.9%−3.0%

4.63E-05+3.0%−3.0%

5.91E-03+9.8%−9.8%

154.0 1.05E-01+4.2%−4.2%

1.19E-02+2.9%−2.9%

4.14E-05+2.9%−3.0%

5.28E-03+9.8%−9.8%

155.0 9.23E-02+4.3%−4.2%

1.05E-02+2.8%−2.9%

3.65E-05+2.9%−2.9%

4.65E-03+9.8%−9.8%

156.0 8.02E-02+4.3%−4.3%

9.15E-03+2.8%−2.8%

3.17E-05+2.8%−2.9%

4.04E-03+9.9%−9.8%

157.0 6.82E-02+4.3%−4.3%

7.79E-03+2.8%−2.8%

2.71E-05+2.8%−2.8%

3.44E-03+9.9%−9.8%

158.0 5.65E-02+4.4%−4.4%

6.46E-03+2.7%−2.8%

2.25E-05+2.8%−2.7%

2.85E-03+9.9%−9.8%

159.0 4.52E-02+4.4%−4.4%

5.17E-03+2.7%−2.7%

1.80E-05+2.8%−2.7%

2.28E-03+9.9%−9.8%

160.0 3.46E-02+4.5%−4.4%

3.96E-03+2.6%−2.7%

1.38E-05+2.7%−2.6%

1.74E-03+9.9%−9.8%

162.0 1.98E-02+4.5%−4.5%

2.27E-03+2.6%−2.7%

7.87E-06+2.7%−2.6%

9.95E-04+9.9%−9.8%

164.0 1.36E-02+4.5%−4.5%

1.56E-03+2.6%−2.7%

5.43E-06+2.7%−2.6%

6.85E-04+9.9%−9.9%

166.0 1.07E-02+4.5%−4.5%

1.24E-03+2.6%−2.6%

4.30E-06+2.7%−2.6%

5.40E-04+9.9%−9.9%

168.0 9.06E-03+4.5%−4.5%

1.05E-03+2.6%−2.6%

3.63E-06+2.6%−2.6%

4.57E-04+9.9%−9.9%

170.0 7.93E-03+4.5%−4.5%

9.20E-04+2.6%−2.6%

3.19E-06+2.6%−2.6%

4.00E-04+9.9%−9.9%

November 18, 2011 – 11 : 26 DRAFT 15

Table 7: SM Higgs branching ratios to two fermions and their total uncertainties (expressed in percentage). Inter-mediate mass range.


172.0 7.10E-03+4.5%−4.5%

8.25E-04+2.6%−2.6%

2.86E-06+2.6%−2.6%

3.57E-04+9.9%−9.9%

174.0 6.45E-03+4.5%−4.5%

7.51E-04+2.6%−2.6%

2.60E-06+2.6%−2.6%

3.25E-04+10.0%−9.9%

176.0 5.91E-03+4.6%−4.5%

6.89E-04+2.6%−2.6%

2.39E-06+2.7%−2.6%

2.97E-04+10.0%−9.9%

178.0 5.44E-03+4.6%−4.5%

6.36E-04+2.6%−2.6%

2.20E-06+2.7%−2.6%

2.74E-04+10.0%−9.9%

180.0 5.01E-03+4.6%−4.5%

5.87E-04+2.6%−2.6%

2.04E-06+2.7%−2.6%

2.52E-04+10.0%−9.9%

182.0 4.55E-03+4.6%−4.5%

5.34E-04+2.6%−2.6%

1.85E-06+2.7%−2.6%

2.29E-04+10.0%−9.9%

184.0 4.09E-03+4.6%−4.5%

4.81E-04+2.6%−2.6%

1.67E-06+2.7%−2.6%

2.06E-04+10.0%−9.9%

186.0 3.70E-03+4.6%−4.5%

4.37E-04+2.6%−2.6%

1.52E-06+2.6%−2.5%

1.87E-04+10.0%−9.9%

188.0 3.41E-03+4.6%−4.5%

4.03E-04+2.6%−2.6%

1.40E-06+2.6%−2.5%

1.72E-04+10.0%−9.9%

190.0 3.17E-03+4.6%−4.6%

3.76E-04+2.6%−2.5%

1.31E-06+2.6%−2.5%

1.59E-04+10.0%−9.8%

192.0 2.97E-03+4.6%−4.6%

3.53E-04+2.6%−2.6%

1.23E-06+2.6%−2.5%

1.50E-04+10.0%−9.9%

194.0 2.80E-03+4.6%−4.6%

3.33E-04+2.6%−2.6%

1.16E-06+2.6%−2.6%

1.41E-04+10.0%−9.9%

196.0 2.65E-03+4.6%−4.6%

3.16E-04+2.6%−2.6%

1.10E-06+2.6%−2.6%

1.34E-04+10.0%−9.9%

198.0 2.52E-03+4.6%−4.6%

3.01E-04+2.6%−2.6%

1.05E-06+2.6%−2.6%

1.27E-04+10.0%−9.9%

200.0 2.40E-03+4.6%−4.6%

2.87E-04+2.5%−2.6%

9.96E-07+2.6%−2.6%

1.21E-04+10.0%−10.0%

202.0 2.29E-03+4.6%−4.6%

2.75E-04+2.6%−2.6%

9.52E-07+2.6%−2.6%

1.16E-04+10.0%−10.0%

204.0 2.19E-03+4.6%−4.6%

2.63E-04+2.6%−2.6%

9.13E-07+2.6%−2.6%

1.11E-04+10.0%−10.0%

206.0 2.10E-03+4.6%−4.6%

2.52E-04+2.6%−2.6%

8.76E-07+2.6%−2.6%

1.06E-04+10.0%−9.9%

208.0 2.01E-03+4.6%−4.6%

2.43E-04+2.6%−2.6%

8.43E-07+2.6%−2.6%

1.02E-04+10.0%−9.9%

210.0 1.93E-03+4.6%−4.6%

2.34E-04+2.6%−2.6%

8.11E-07+2.6%−2.6%

9.75E-05+10.0%−9.9%

212.0 1.87E-03+4.6%−4.6%

2.25E-04+2.6%−2.6%

7.81E-07+2.6%−2.6%

9.38E-05+10.0%−9.9%

214.0 1.80E-03+4.7%−4.6%

2.18E-04+2.6%−2.6%

7.54E-07+2.6%−2.6%

9.04E-05+10.1%−9.9%

216.0 1.73E-03+4.7%−4.6%

2.10E-04+2.6%−2.6%

7.29E-07+2.6%−2.6%

8.71E-05+10.1%−9.9%

218.0 1.67E-03+4.7%−4.5%

2.03E-04+2.6%−2.6%

7.04E-07+2.6%−2.6%

8.41E-05+10.1%−9.9%

220.0 1.61E-03+4.7%−4.5%

1.97E-04+2.6%−2.6%

6.81E-07+2.6%−2.6%

8.11E-05+10.1%−9.9%

222.0 1.56E-03+4.7%−4.5%

1.90E-04+2.6%−2.6%

6.59E-07+2.6%−2.6%

7.84E-05+10.1%−9.9%

224.0 1.51E-03+4.7%−4.5%

1.84E-04+2.6%−2.6%

6.39E-07+2.6%−2.6%

7.59E-05+10.1%−9.9%

226.0 1.46E-03+4.7%−4.5%

1.79E-04+2.6%−2.6%

6.19E-07+2.6%−2.6%

7.34E-05+10.1%−10.0%

228.0 1.41E-03+4.7%−4.5%

1.73E-04+2.6%−2.6%

6.00E-07+2.6%−2.6%

7.10E-05+10.1%−10.0%

230.0 1.37E-03+4.7%−4.5%

1.68E-04+2.6%−2.6%

5.82E-07+2.6%−2.6%

6.88E-05+10.1%−10.0%

232.0 1.33E-03+4.7%−4.5%

1.63E-04+2.6%−2.6%

5.65E-07+2.6%−2.6%

6.67E-05+10.1%−10.0%

234.0 1.29E-03+4.7%−4.5%

1.58E-04+2.6%−2.6%

5.49E-07+2.6%−2.6%

6.46E-05+10.1%−10.0%

236.0 1.25E-03+4.7%−4.5%

1.54E-04+2.6%−2.6%

5.33E-07+2.6%−2.6%

6.27E-05+10.1%−10.0%

238.0 1.21E-03+4.7%−4.5%

1.49E-04+2.6%−2.6%

5.19E-07+2.6%−2.6%

6.09E-05+10.1%−10.0%

240.0 1.17E-03+4.7%−4.5%

1.45E-04+2.6%−2.6%

5.05E-07+2.6%−2.6%

5.92E-05+10.1%−10.0%

242.0 1.14E-03+4.7%−4.6%

1.41E-04+2.6%−2.6%

4.91E-07+2.6%−2.6%

5.75E-05+10.1%−10.0%

244.0 1.11E-03+4.7%−4.6%

1.38E-04+2.6%−2.6%

4.78E-07+2.6%−2.6%

5.59E-05+10.1%−10.0%

246.0 1.08E-03+4.7%−4.6%

1.34E-04+2.6%−2.6%

4.66E-07+2.6%−2.6%

5.43E-05+10.1%−10.0%

248.0 1.05E-03+4.7%−4.6%

1.31E-04+2.6%−2.7%

4.53E-07+2.6%−2.6%

5.28E-05+10.1%−10.0%

250.0 1.02E-03+4.7%−4.6%

1.27E-04+2.6%−2.7%

4.42E-07+2.6%−2.6%

5.14E-05+10.1%−10.0%

252.0 9.95E-04+4.7%−4.6%

1.24E-04+2.6%−2.7%

4.31E-07+2.6%−2.6%

5.00E-05+10.1%−10.0%

254.0 9.69E-04+4.7%−4.6%

1.21E-04+2.6%−2.6%

4.20E-07+2.6%−2.6%

4.87E-05+10.1%−10.0%

256.0 9.43E-04+4.7%−4.6%

1.18E-04+2.6%−2.6%

4.10E-07+2.6%−2.6%

4.74E-05+10.1%−10.0%

258.0 9.19E-04+4.7%−4.6%

1.15E-04+2.6%−2.6%

4.00E-07+2.6%−2.6%

4.62E-05+10.1%−10.0%

260.0 8.96E-04+4.7%−4.6%

1.12E-04+2.6%−2.6%

3.90E-07+2.6%−2.6%

4.51E-05+10.1%−10.0%

November 18, 2011 – 11 : 26 DRAFT 16

Table 8: SM Higgs branching ratios to two fermions and their total uncertainties (expressed in percentage). Highmass range.

MH [GeV] H → bb H → τ+τ− H → µ+µ− H → cc H → tt

262.0 8.74E-04+4.7%−4.6%

1.10E-04+2.6%−2.6%

3.81E-07+2.6%−2.6%

4.39E-05+10.1%−10.0%

1.89E-07+342.0%−102.1%

264.0 8.52E-04+4.7%−4.6%

1.07E-04+2.6%−2.6%

3.72E-07+2.6%−2.6%

4.28E-05+10.1%−10.0%

4.49E-07+276.1%−91.5%

266.0 8.31E-04+4.7%−4.6%

1.05E-04+2.6%−2.6%

3.63E-07+2.6%−2.6%

4.18E-05+10.1%−10.0%

8.63E-07+210.1%−80.9%

268.0 8.11E-04+4.7%−4.6%

1.02E-04+2.6%−2.6%

3.55E-07+2.6%−2.6%

4.08E-05+10.1%−10.0%

1.46E-06+144.1%−70.3%

270.0 7.92E-04+4.7%−4.6%

1.00E-04+2.6%−2.6%

3.47E-07+2.6%−2.6%

3.98E-05+10.1%−10.0%

2.29E-06+78.1%−59.7%

272.0 7.73E-04+4.7%−4.6%

9.80E-05+2.6%−2.6%

3.40E-07+2.6%−2.6%

3.89E-05+10.1%−10.0%

3.37E-06+72.3%−56.6%

274.0 7.55E-04+4.7%−4.6%

9.58E-05+2.6%−2.6%

3.32E-07+2.6%−2.6%

3.80E-05+10.1%−10.0%

4.72E-06+66.5%−53.6%

276.0 7.38E-04+4.7%−4.6%

9.37E-05+2.6%−2.6%

3.25E-07+2.6%−2.6%

3.71E-05+10.1%−10.0%

6.41E-06+60.7%−50.6%

278.0 7.21E-04+4.7%−4.7%

9.17E-05+2.6%−2.6%

3.18E-07+2.6%−2.6%

3.63E-05+10.1%−10.0%

8.45E-06+54.9%−47.5%

280.0 7.05E-04+4.7%−4.7%

8.98E-05+2.6%−2.6%

3.11E-07+2.6%−2.6%

3.55E-05+10.1%−10.0%

1.09E-05+49.2%−44.5%

282.0 6.90E-04+4.7%−4.7%

8.79E-05+2.6%−2.6%

3.05E-07+2.6%−2.6%

3.47E-05+10.1%−10.0%

1.37E-05+47.2%−43.2%

284.0 6.74E-04+4.7%−4.7%

8.61E-05+2.6%−2.6%

2.98E-07+2.6%−2.6%

3.39E-05+10.1%−10.0%

1.72E-05+45.2%−41.9%

286.0 6.60E-04+4.7%−4.7%

8.43E-05+2.6%−2.6%

2.92E-07+2.6%−2.6%

3.32E-05+10.2%−10.0%

2.11E-05+43.2%−40.6%

288.0 6.46E-04+4.7%−4.7%

8.26E-05+2.6%−2.6%

2.86E-07+2.6%−2.6%

3.25E-05+10.2%−10.0%

2.55E-05+41.3%−39.4%

290.0 6.32E-04+4.7%−4.7%

8.09E-05+2.6%−2.6%

2.81E-07+2.6%−2.6%

3.18E-05+10.2%−10.0%

3.06E-05+39.3%−38.1%

295.0 6.00E-04+4.7%−4.7%

7.70E-05+2.6%−2.6%

2.67E-07+2.6%−2.6%

3.01E-05+10.1%−10.0%

4.67E-05+37.3%−36.6%

300.0 5.70E-04+4.7%−4.7%

7.33E-05+2.6%−2.6%

2.55E-07+2.6%−2.6%

2.86E-05+10.1%−10.0%

6.87E-05+35.3%−35.1%

305.0 5.42E-04+4.7%−4.7%

7.00E-05+2.6%−2.6%

2.43E-07+2.6%−2.6%

2.72E-05+10.2%−10.0%

9.83E-05+35.0%−34.5%

310.0 5.15E-04+4.7%−4.7%

6.69E-05+2.6%−2.6%

2.32E-07+2.6%−2.6%

2.60E-05+10.2%−10.0%

1.38E-04+34.6%−33.9%

315.0 4.92E-04+4.8%−4.6%

6.40E-05+2.6%−2.5%

2.22E-07+2.7%−2.5%

2.48E-05+10.2%−10.0%

1.91E-04+35.7%−34.1%

320.0 4.69E-04+4.8%−4.6%

6.11E-05+2.7%−2.5%

2.12E-07+2.7%−2.5%

2.35E-05+10.2%−10.0%

2.65E-04+36.8%−34.4%

325.0 4.49E-04+4.8%−4.6%

5.86E-05+2.6%−2.5%

2.03E-07+2.6%−2.5%

2.25E-05+10.2%−10.0%

3.70E-04+41.0%−35.7%

330.0 4.30E-04+4.8%−4.7%

5.63E-05+2.6%−2.5%

1.95E-07+2.6%−2.5%

2.16E-05+10.2%−10.1%

5.22E-04+45.1%−37.1%

335.0 4.12E-04+4.8%−4.7%

5.41E-05+2.6%−2.5%

1.87E-07+2.6%−2.5%

2.07E-05+10.2%−10.1%

7.61E-04+110.4%−41.5%

340.0 3.95E-04+4.8%−4.7%

5.20E-05+2.7%−2.5%

1.80E-07+2.7%−2.5%

1.98E-05+10.1%−10.1%

1.20E-03+175.6%−45.9%

345.0 3.80E-04+5.0%−5.0%

5.02E-05+3.5%−3.7%

1.74E-07+3.5%−3.7%

1.91E-05+10.3%−10.3%

3.28E-03+151.7%−68.6%

350.0 3.60E-04+5.2%−5.3%

4.77E-05+4.2%−4.9%

1.65E-07+4.2%−4.9%

1.81E-05+10.5%−10.4%

1.56E-02+127.8%−91.3%

360.0 3.18E-04+6.0%−5.4%

4.23E-05+5.6%−4.9%

1.47E-07+5.6%−4.9%

1.60E-05+11.2%−10.4%

5.14E-02+42.2%−48.4%

370.0 2.83E-04+6.4%−5.3%

3.78E-05+5.8%−4.7%

1.31E-07+5.8%−4.8%

1.42E-05+11.6%−10.4%

8.35E-02+25.4%−32.1%

380.0 2.54E-04+6.6%−5.4%

3.41E-05+5.8%−4.6%

1.18E-07+5.8%−4.6%

1.28E-05+11.8%−10.6%

1.10E-01+18.4%−24.7%

390.0 2.30E-04+6.7%−5.4%

3.10E-05+5.8%−4.5%

1.07E-07+5.9%−4.5%

1.16E-05+12.0%−10.7%

1.31E-01+14.5%−20.6%

400.0 2.10E-04+6.8%−5.5%

2.84E-05+5.8%−4.3%

9.83E-08+5.8%−4.3%

1.05E-05+12.2%−10.8%

1.48E-01+12.2%−17.8%

410.0 1.93E-04+6.9%−5.5%

2.62E-05+5.7%−4.3%

9.07E-08+5.7%−4.2%

9.66E-06+12.3%−10.8%

1.61E-01+10.4%−16.1%

420.0 1.78E-04+7.0%−5.5%

2.43E-05+5.6%−4.1%

8.41E-08+5.6%−4.1%

8.93E-06+12.4%−10.9%

1.71E-01+9.3%−14.7%

430.0 1.65E-04+7.0%−5.6%

2.27E-05+5.5%−4.0%

7.84E-08+5.5%−4.0%

8.29E-06+12.5%−10.9%

1.79E-01+8.4%−13.8%

440.0 1.54E-04+7.1%−5.6%

2.12E-05+5.4%−3.9%

7.34E-08+5.4%−3.9%

7.73E-06+12.5%−10.9%

1.84E-01+7.7%−13.0%

450.0 1.44E-04+7.2%−5.6%

2.00E-05+5.3%−3.8%

6.91E-08+5.3%−3.8%

7.25E-06+12.6%−11.0%

1.88E-01+7.2%−12.4%

460.0 1.36E-04+7.2%−5.7%

1.88E-05+5.2%−3.7%

6.52E-08+5.3%−3.7%

6.82E-06+12.6%−11.0%

1.91E-01+6.8%−11.9%

470.0 1.28E-04+7.2%−5.6%

1.78E-05+5.2%−3.6%

6.17E-08+5.2%−3.6%

6.43E-06+12.6%−11.0%

1.92E-01+6.4%−11.6%

480.0 1.21E-04+7.2%−5.5%

1.69E-05+5.1%−3.6%

5.86E-08+5.1%−3.5%

6.08E-06+12.6%−11.0%

1.93E-01+6.1%−11.2%

490.0 1.15E-04+7.2%−5.5%

1.61E-05+5.0%−3.5%

5.57E-08+5.0%−3.5%

5.76E-06+12.6%−11.0%

1.93E-01+5.9%−11.0%

500.0 1.09E-04+7.2%−5.4%

1.53E-05+5.0%−3.2%

5.31E-08+5.1%−3.1%

5.47E-06+12.8%−10.7%

1.92E-01+4.6%−9.8%

510.0 1.04E-04+7.4%−5.3%

1.46E-05+5.1%−3.1%

5.07E-08+5.1%−3.1%

5.21E-06+12.8%−10.8%

1.91E-01+4.7%−9.8%

520.0 9.88E-05+7.5%−5.4%

1.40E-05+5.1%−3.2%

4.85E-08+5.1%−3.1%

4.96E-06+12.9%−10.8%

1.90E-01+4.8%−10.1%

530.0 9.44E-05+7.5%−5.5%

1.34E-05+5.3%−3.3%

4.64E-08+5.2%−3.2%

4.74E-06+13.0%−10.9%

1.88E-01+5.0%−10.4%

540.0 9.02E-05+7.6%−5.6%

1.29E-05+5.4%−3.4%

4.44E-08+5.4%−3.4%

4.52E-06+13.1%−11.0%

1.85E-01+5.2%−10.7%

November 18, 2011 – 11 : 26 DRAFT 17

Table 9: SM Higgs branching ratios to two fermions and their total uncertainties (expressed in percentage). Veryhigh mass range.

MH [GeV] H → bb H → τ+τ− H → µ+µ− H → cc H → tt

550.0 8.64E-05+7.7%−5.7%

1.23E-05+5.5%−3.5%

4.27E-08+5.5%−3.5%

4.33E-06+13.1%−11.1%

1.83E-01+5.4%−10.9%

560.0 8.28E-05+7.8%−5.8%

1.19E-05+5.6%−3.7%

4.10E-08+5.6%−3.6%

4.15E-06+13.2%−11.2%

1.80E-01+5.6%−11.3%

570.0 7.95E-05+7.8%−5.9%

1.14E-05+5.8%−3.7%

3.95E-08+5.7%−3.8%

3.98E-06+13.3%−11.3%

1.78E-01+5.7%−11.6%

580.0 7.64E-05+7.9%−6.0%

1.10E-05+5.8%−4.0%

3.80E-08+5.8%−4.0%

3.83E-06+13.4%−11.4%

1.75E-01+5.9%−11.9%

590.0 7.34E-05+8.1%−6.1%

1.06E-05+6.0%−4.0%

3.67E-08+6.0%−4.0%

3.68E-06+13.5%−11.5%

1.72E-01+6.2%−12.2%

600.0 7.06E-05+8.2%−6.3%

1.02E-05+6.2%−4.2%

3.54E-08+6.1%−4.2%

3.54E-06+13.7%−11.6%

1.69E-01+6.3%−12.4%

610.0 6.81E-05+8.3%−6.5%

9.87E-06+6.2%−4.4%

3.42E-08+6.2%−4.4%

3.41E-06+13.8%−11.8%

1.66E-01+6.4%−12.8%

620.0 6.55E-05+8.4%−6.6%

9.53E-06+6.3%−4.5%

3.30E-08+6.3%−4.5%

3.29E-06+13.9%−12.0%

1.63E-01+6.6%−13.2%

630.0 6.32E-05+8.6%−6.7%

9.22E-06+6.5%−4.7%

3.19E-08+6.6%−4.7%

3.17E-06+14.0%−12.1%

1.59E-01+6.8%−13.4%

640.0 6.10E-05+8.8%−6.9%

8.92E-06+6.7%−4.9%

3.09E-08+6.7%−4.9%

3.06E-06+14.2%−12.3%

1.56E-01+7.0%−13.8%

650.0 5.89E-05+8.9%−7.1%

8.63E-06+6.8%−5.0%

2.99E-08+6.8%−5.0%

2.95E-06+14.4%−12.4%

1.53E-01+7.1%−14.2%

660.0 5.69E-05+9.1%−7.2%

8.36E-06+7.0%−5.2%

2.90E-08+7.0%−5.2%

2.85E-06+14.5%−12.6%

1.50E-01+7.2%−14.6%

670.0 5.50E-05+9.3%−7.4%

8.10E-06+7.2%−5.4%

2.81E-08+7.2%−5.4%

2.76E-06+14.8%−12.8%

1.47E-01+7.5%−15.0%

680.0 5.32E-05+9.5%−7.6%

7.85E-06+7.4%−5.5%

2.72E-08+7.4%−5.5%

2.67E-06+14.9%−13.0%

1.44E-01+7.7%−15.4%

690.0 5.15E-05+9.7%−7.8%

7.61E-06+7.6%−5.8%

2.64E-08+7.5%−5.8%

2.58E-06+15.1%−13.2%

1.41E-01+7.8%−15.8%

700.0 4.98E-05+9.9%−8.0%

7.38E-06+7.8%−6.0%

2.56E-08+7.8%−6.0%

2.50E-06+15.3%−13.4%

1.38E-01+8.0%−16.2%

710.0 4.82E-05+10.1%−8.2%

7.16E-06+8.0%−6.2%

2.48E-08+8.0%−6.2%

2.42E-06+15.6%−13.7%

1.35E-01+8.2%−16.7%

720.0 4.67E-05+10.4%−8.4%

6.94E-06+8.3%−6.4%

2.41E-08+8.3%−6.4%

2.34E-06+15.8%−13.8%

1.32E-01+8.4%−17.1%

730.0 4.53E-05+10.6%−8.7%

6.74E-06+8.5%−6.6%

2.34E-08+8.5%−6.7%

2.27E-06+16.0%−14.1%

1.29E-01+8.6%−17.6%

740.0 4.38E-05+10.9%−8.9%

6.55E-06+8.8%−6.9%

2.27E-08+8.8%−6.8%

2.20E-06+16.3%−14.4%

1.26E-01+8.7%−18.2%

750.0 4.24E-05+11.2%−9.2%

6.36E-06+9.1%−7.1%

2.21E-08+9.1%−7.1%

2.13E-06+16.6%−14.6%

1.23E-01+8.9%−18.7%

760.0 4.11E-05+11.4%−9.4%

6.18E-06+9.3%−7.4%

2.15E-08+9.3%−7.3%

2.07E-06+16.9%−14.8%

1.20E-01+9.2%−19.2%

770.0 3.99E-05+11.8%−9.7%

6.01E-06+9.6%−7.6%

2.09E-08+9.6%−7.6%

2.00E-06+17.2%−15.0%

1.18E-01+9.4%−19.8%

780.0 3.87E-05+12.1%−10.0%

5.84E-06+10.0%−7.9%

2.03E-08+10.0%−7.9%

1.94E-06+17.6%−15.3%

1.15E-01+9.7%−20.4%

790.0 3.75E-05+12.5%−10.2%

5.67E-06+10.4%−8.2%

1.97E-08+10.3%−8.1%

1.89E-06+17.9%−15.6%

1.12E-01+10.1%−20.9%

800.0 3.64E-05+12.8%−10.5%

5.52E-06+10.7%−8.5%

1.92E-08+10.7%−8.5%

1.83E-06+18.3%−15.9%

1.10E-01+10.6%−21.6%

810.0 3.54E-05+13.2%−10.8%

5.37E-06+11.1%−8.8%

1.86E-08+11.1%−8.8%

1.78E-06+18.7%−16.2%

1.07E-01+11.0%−22.3%

820.0 3.43E-05+13.7%−11.1%

5.22E-06+11.5%−9.1%

1.81E-08+11.5%−9.1%

1.73E-06+19.1%−16.5%

1.05E-01+11.5%−23.0%

830.0 3.33E-05+14.1%−11.4%

5.08E-06+11.9%−9.4%

1.76E-08+11.8%−9.4%

1.68E-06+19.5%−16.8%

1.02E-01+12.0%−23.6%

840.0 3.24E-05+14.5%−11.8%

4.94E-06+12.3%−9.7%

1.72E-08+12.3%−9.7%

1.63E-06+19.9%−17.2%

9.99E-02+12.5%−24.3%

850.0 3.14E-05+15.0%−12.1%

4.80E-06+12.8%−10.0%

1.67E-08+12.8%−10.1%

1.58E-06+20.4%−17.5%

9.76E-02+12.9%−25.1%

860.0 3.05E-05+15.4%−12.5%

4.67E-06+13.3%−10.4%

1.62E-08+13.3%−10.4%

1.54E-06+20.9%−17.9%

9.52E-02+13.5%−25.8%

870.0 2.97E-05+15.9%−12.9%

4.55E-06+13.8%−10.7%

1.58E-08+13.8%−10.8%

1.49E-06+21.4%−18.3%

9.29E-02+14.0%−26.6%

880.0 2.88E-05+16.5%−13.2%

4.43E-06+14.3%−11.1%

1.54E-08+14.3%−11.1%

1.45E-06+22.0%−18.6%

9.07E-02+14.6%−27.4%

890.0 2.80E-05+17.0%−13.6%

4.31E-06+14.9%−11.5%

1.50E-08+14.9%−11.5%

1.41E-06+22.5%−19.1%

8.86E-02+15.1%−28.3%

900.0 2.72E-05+17.6%−14.0%

4.19E-06+15.5%−11.9%

1.46E-08+15.5%−11.8%

1.37E-06+23.1%−19.4%

8.65E-02+15.8%−29.2%

910.0 2.64E-05+18.2%−14.4%

4.08E-06+16.1%−12.3%

1.42E-08+16.0%−12.3%

1.33E-06+23.8%−19.8%

8.44E-02+16.4%−30.1%

920.0 2.57E-05+18.9%−14.8%

3.97E-06+16.7%−12.7%

1.38E-08+16.7%−12.7%

1.29E-06+24.3%−20.2%

8.23E-02+17.0%−31.0%

930.0 2.49E-05+19.6%−15.2%

3.87E-06+17.4%−13.1%

1.34E-08+17.4%−13.1%

1.25E-06+25.1%−20.6%

8.03E-02+17.6%−32.0%

940.0 2.42E-05+20.3%−15.6%

3.76E-06+18.1%−13.5%

1.31E-08+18.1%−13.5%

1.22E-06+25.7%−21.1%

7.83E-02+18.3%−33.0%

950.0 2.35E-05+21.0%−16.1%

3.66E-06+18.8%−14.0%

1.27E-08+18.9%−13.9%

1.18E-06+26.6%−21.5%

7.64E-02+19.0%−34.0%

960.0 2.29E-05+21.9%−16.6%

3.56E-06+19.6%−14.4%

1.24E-08+19.7%−14.3%

1.15E-06+27.3%−21.9%

7.45E-02+19.8%−35.0%

970.0 2.23E-05+22.7%−17.0%

3.47E-06+20.4%−14.9%

1.21E-08+20.5%−14.8%

1.12E-06+28.2%−22.4%

7.26E-02+20.5%−36.1%

980.0 2.17E-05+23.5%−17.5%

3.38E-06+21.3%−15.3%

1.17E-08+21.2%−15.3%

1.09E-06+28.9%−22.9%

7.08E-02+21.2%−37.2%

990.0 2.11E-05+24.4%−18.0%

3.28E-06+22.2%−15.8%

1.14E-08+22.2%−15.8%

1.06E-06+29.9%−23.4%

6.90E-02+22.1%−38.3%

1000.0 2.05E-05+25.3%−18.5%

3.20E-06+23.1%−16.3%

1.11E-08+23.1%−16.3%

1.03E-06+30.9%−23.8%

6.73E-02+22.9%−39.5%

November 18, 2011 – 11 : 26 DRAFT 18

Table 10: SM Higgs branching ratios to two gauge bosons and Higgs totalwidth together with their total uncer-tainties (expressed in percentage). Very low mass range.

MH [GeV] H → gg H → γγ H → Zγ H → WW H → ZZ ΓH [GeV]

90.0 6.12E-02+11.8%−11.4%

1.22E-03+6.2%−6.2%

0.00E+00+0.0%−0.0%

2.07E-03+5.8%−5.7%

4.17E-04+5.8%−5.6%

2.22E-03+5.2%−5.2%

95.0 6.74E-02+11.7%−11.3%

1.39E-03+6.2%−6.1%

4.48E-06+10.2%−10.1%

4.67E-03+5.8%−5.6%

6.65E-04+5.7%−5.6%

2.35E-03+5.2%−5.1%

100.0 7.36E-02+11.6%−11.2%

1.58E-03+6.2%−6.1%

4.93E-05+10.2%−10.1%

1.09E-02+5.7%−5.6%

1.12E-03+5.7%−5.5%

2.49E-03+5.1%−5.1%

105.0 7.95E-02+11.4%−11.1%

1.77E-03+6.1%−5.9%

1.71E-04+10.2%−9.9%

2.40E-02+5.6%−5.5%

2.13E-03+5.6%−5.5%

2.65E-03+5.1%−5.0%

110.0 8.45E-02+11.2%−10.9%

1.95E-03+5.9%−5.8%

3.91E-04+9.9%−9.8%

4.77E-02+5.4%−5.3%

4.34E-03+5.4%−5.3%

2.85E-03+4.9%−4.9%

110.5 8.49E-02+11.2%−10.8%

1.97E-03+5.9%−5.8%

4.18E-04+9.9%−9.8%

5.09E-02+5.4%−5.3%

4.67E-03+5.4%−5.3%

2.87E-03+4.9%−4.9%

111.0 8.53E-02+11.2%−10.8%

1.98E-03+5.9%−5.8%

4.47E-04+9.9%−9.8%

5.40E-02+5.4%−5.2%

5.00E-03+5.4%−5.2%

2.90E-03+4.9%−4.8%

111.5 8.56E-02+11.1%−10.8%

2.00E-03+5.9%−5.8%

4.76E-04+9.9%−9.8%

5.75E-02+5.4%−5.2%

5.38E-03+5.3%−5.2%

2.92E-03+4.8%−4.8%

112.0 8.60E-02+11.1%−10.8%

2.02E-03+5.8%−5.8%

5.07E-04+9.8%−9.7%

6.10E-02+5.3%−5.2%

5.76E-03+5.3%−5.2%

2.95E-03+4.8%−4.8%

112.5 8.63E-02+11.1%−10.8%

2.03E-03+5.8%−5.7%

5.39E-04+9.8%−9.7%

6.47E-02+5.3%−5.2%

6.17E-03+5.3%−5.2%

2.98E-03+4.8%−4.8%

113.0 8.66E-02+11.1%−10.7%

2.05E-03+5.8%−5.7%

5.72E-04+9.8%−9.7%

6.87E-02+5.3%−5.2%

6.62E-03+5.3%−5.1%

3.00E-03+4.8%−4.8%

113.5 8.69E-02+11.0%−10.7%

2.07E-03+5.8%−5.7%

6.05E-04+9.8%−9.7%

7.27E-02+5.2%−5.1%

7.08E-03+5.2%−5.1%

3.03E-03+4.8%−4.7%

114.0 8.72E-02+11.0%−10.7%

2.08E-03+5.8%−5.6%

6.39E-04+9.7%−9.7%

7.70E-02+5.2%−5.1%

7.58E-03+5.2%−5.1%

3.06E-03+4.7%−4.7%

114.5 8.74E-02+11.0%−10.7%

2.10E-03+5.8%−5.6%

6.74E-04+9.7%−9.6%

8.14E-02+5.2%−5.1%

8.10E-03+5.2%−5.1%

3.09E-03+4.7%−4.7%

115.0 8.76E-02+10.9%−10.6%

2.11E-03+5.7%−5.6%

7.10E-04+9.7%−9.6%

8.60E-02+5.2%−5.0%

8.65E-03+5.2%−5.0%

3.12E-03+4.7%−4.7%

115.5 8.78E-02+10.9%−10.6%

2.12E-03+5.7%−5.6%

7.46E-04+9.7%−9.6%

9.05E-02+5.1%−5.0%

9.21E-03+5.1%−5.0%

3.16E-03+4.7%−4.6%

116.0 8.80E-02+10.9%−10.6%

2.14E-03+5.7%−5.5%

7.84E-04+9.6%−9.6%

9.55E-02+5.1%−5.0%

9.83E-03+5.1%−5.0%

3.19E-03+4.6%−4.6%

116.5 8.81E-02+10.8%−10.5%

2.15E-03+5.6%−5.5%

8.22E-04+9.6%−9.5%

1.01E-01+5.0%−4.9%

1.05E-02+5.0%−4.9%

3.23E-03+4.6%−4.6%

117.0 8.82E-02+10.8%−10.5%

2.16E-03+5.6%−5.5%

8.61E-04+9.6%−9.5%

1.06E-01+5.0%−4.9%

1.12E-02+5.0%−4.9%

3.26E-03+4.6%−4.5%

117.5 8.83E-02+10.8%−10.5%

2.18E-03+5.6%−5.4%

9.00E-04+9.5%−9.5%

1.11E-01+5.0%−4.8%

1.19E-02+5.0%−4.8%

3.30E-03+4.5%−4.5%

118.0 8.83E-02+10.8%−10.4%

2.19E-03+5.5%−5.4%

9.40E-04+9.5%−9.4%

1.17E-01+4.9%−4.8%

1.26E-02+4.9%−4.8%

3.34E-03+4.5%−4.5%

118.5 8.83E-02+10.7%−10.4%

2.20E-03+5.5%−5.4%

9.81E-04+9.5%−9.4%

1.23E-01+4.9%−4.8%

1.34E-02+4.9%−4.8%

3.37E-03+4.5%−4.4%

119.0 8.83E-02+10.7%−10.4%

2.21E-03+5.5%−5.3%

1.02E-03+9.4%−9.4%

1.29E-01+4.8%−4.7%

1.42E-02+4.8%−4.7%

3.41E-03+4.4%−4.4%

119.5 8.84E-02+10.7%−10.4%

2.22E-03+5.4%−5.3%

1.06E-03+9.4%−9.4%

1.35E-01+4.8%−4.7%

1.50E-02+4.8%−4.7%

3.46E-03+4.4%−4.4%

120.0 8.82E-02+10.6%−10.3%

2.23E-03+5.4%−5.3%

1.11E-03+9.4%−9.3%

1.41E-01+4.8%−4.7%

1.59E-02+4.8%−4.7%

3.50E-03+4.4%−4.3%

120.5 8.82E-02+10.6%−10.3%

2.23E-03+5.4%−5.2%

1.15E-03+9.3%−9.3%

1.48E-01+4.7%−4.6%

1.68E-02+4.7%−4.6%

3.55E-03+4.3%−4.3%

121.0 8.80E-02+10.6%−10.3%

2.24E-03+5.3%−5.2%

1.19E-03+9.3%−9.2%

1.55E-01+4.7%−4.6%

1.77E-02+4.7%−4.6%

3.60E-03+4.3%−4.2%

121.5 8.79E-02+10.5%−10.2%

2.25E-03+5.3%−5.2%

1.23E-03+9.3%−9.2%

1.61E-01+4.6%−4.5%

1.87E-02+4.6%−4.5%

3.65E-03+4.2%−4.2%

122.0 8.77E-02+10.5%−10.2%

2.25E-03+5.2%−5.1%

1.28E-03+9.2%−9.1%

1.69E-01+4.6%−4.5%

1.97E-02+4.6%−4.5%

3.70E-03+4.2%−4.2%

122.5 8.74E-02+10.4%−10.2%

2.26E-03+5.2%−5.1%

1.32E-03+9.2%−9.1%

1.76E-01+4.5%−4.4%

2.07E-02+4.5%−4.4%

3.76E-03+4.2%−4.1%

123.0 8.71E-02+10.4%−10.1%

2.27E-03+5.2%−5.0%

1.36E-03+9.2%−9.0%

1.83E-01+4.5%−4.4%

2.18E-02+4.5%−4.4%

3.82E-03+4.1%−4.1%

123.5 8.68E-02+10.3%−10.1%

2.28E-03+5.1%−5.0%

1.41E-03+9.1%−9.0%

1.91E-01+4.4%−4.3%

2.29E-02+4.5%−4.3%

3.88E-03+4.1%−4.0%

124.0 8.65E-02+10.3%−10.1%

2.28E-03+5.1%−5.0%

1.45E-03+9.1%−8.9%

1.98E-01+4.4%−4.3%

2.40E-02+4.4%−4.3%

3.94E-03+4.0%−4.0%

124.5 8.61E-02+10.3%−10.0%

2.28E-03+5.0%−4.9%

1.49E-03+9.1%−8.9%

2.07E-01+4.3%−4.2%

2.52E-02+4.4%−4.2%

4.00E-03+4.0%−4.0%

125.0 8.57E-02+10.2%−10.0%

2.28E-03+5.0%−4.9%

1.54E-03+9.0%−8.8%

2.15E-01+4.3%−4.2%

2.64E-02+4.3%−4.2%

4.07E-03+4.0%−3.9%

125.5 8.52E-02+10.2%−9.9%

2.28E-03+4.9%−4.8%

1.58E-03+8.9%−8.8%

2.23E-01+4.2%−4.1%

2.76E-02+4.3%−4.1%

4.14E-03+3.9%−3.9%

126.0 8.48E-02+10.1%−9.9%

2.28E-03+4.9%−4.8%

1.62E-03+8.9%−8.8%

2.31E-01+4.1%−4.1%

2.89E-02+4.2%−4.0%

4.21E-03+3.9%−3.8%

126.5 8.42E-02+10.1%−9.8%

2.28E-03+4.8%−4.7%

1.66E-03+8.8%−8.7%

2.39E-01+4.1%−4.0%

3.02E-02+4.1%−4.0%

4.29E-03+3.8%−3.8%

127.0 8.37E-02+10.1%−9.8%

2.28E-03+4.8%−4.7%

1.70E-03+8.8%−8.7%

2.48E-01+4.0%−4.0%

3.15E-02+4.1%−3.9%

4.37E-03+3.8%−3.7%

127.5 8.31E-02+10.0%−9.8%

2.28E-03+4.8%−4.6%

1.75E-03+8.7%−8.6%

2.57E-01+4.0%−3.9%

3.28E-02+4.0%−3.9%

4.45E-03+3.7%−3.7%

128.0 8.25E-02+10.0%−9.7%

2.27E-03+4.7%−4.6%

1.79E-03+8.7%−8.6%

2.66E-01+3.9%−3.9%

3.42E-02+3.9%−3.8%

4.53E-03+3.7%−3.6%

128.5 8.19E-02+9.9%−9.7%

2.27E-03+4.7%−4.5%

1.83E-03+8.6%−8.6%

2.75E-01+3.8%−3.8%

3.56E-02+3.9%−3.8%

4.62E-03+3.6%−3.6%

129.0 8.12E-02+9.9%−9.6%

2.26E-03+4.6%−4.5%

1.87E-03+8.5%−8.5%

2.84E-01+3.8%−3.7%

3.70E-02+3.8%−3.7%

4.71E-03+3.6%−3.5%

129.5 8.05E-02+9.8%−9.6%

2.26E-03+4.6%−4.4%

1.90E-03+8.5%−8.5%

2.93E-01+3.7%−3.7%

3.84E-02+3.7%−3.7%

4.81E-03+3.5%−3.5%

130.0 7.97E-02+9.8%−9.6%

2.25E-03+4.5%−4.4%

1.95E-03+8.4%−8.4%

3.03E-01+3.7%−3.6%

3.98E-02+3.7%−3.6%

4.91E-03+3.5%−3.4%

November 18, 2011 – 11 : 26 DRAFT 19

Table 11: SM Higgs branching ratios to two gauge bosons and Higgs totalwidth together with their total uncer-tainties (expressed in percentage). Low and intermediate mass range.


130.5 7.90E-02+9.8%−9.5%

2.24E-03+4.5%−4.3%

1.99E-03+8.4%−8.4%

3.12E-01+3.6%−3.5%

4.13E-02+3.6%−3.5%

5.01E-03+3.4%−3.4%

131.0 7.82E-02+9.7%−9.5%

2.23E-03+4.4%−4.3%

2.01E-03+8.3%−8.3%

3.22E-01+3.5%−3.5%

4.28E-02+3.5%−3.5%

5.12E-03+3.4%−3.3%

131.5 7.73E-02+9.7%−9.4%

2.22E-03+4.4%−4.2%

2.06E-03+8.3%−8.3%

3.31E-01+3.5%−3.4%

4.42E-02+3.5%−3.4%

5.23E-03+3.3%−3.3%

132.0 7.65E-02+9.6%−9.4%

2.21E-03+4.3%−4.2%

2.09E-03+8.2%−8.2%

3.41E-01+3.4%−3.4%

4.57E-02+3.4%−3.4%

5.35E-03+3.2%−3.2%

132.5 7.56E-02+9.6%−9.4%

2.20E-03+4.2%−4.1%

2.13E-03+8.2%−8.2%

3.51E-01+3.3%−3.3%

4.72E-02+3.3%−3.3%

5.47E-03+3.2%−3.2%

133.0 7.47E-02+9.5%−9.3%

2.19E-03+4.2%−4.1%

2.16E-03+8.1%−8.1%

3.61E-01+3.3%−3.2%

4.87E-02+3.3%−3.2%

5.60E-03+3.1%−3.1%

133.5 7.37E-02+9.5%−9.3%

2.17E-03+4.1%−4.0%

2.19E-03+8.1%−8.1%

3.70E-01+3.2%−3.2%

5.02E-02+3.2%−3.2%

5.74E-03+3.1%−3.1%

134.0 7.28E-02+9.4%−9.2%

2.16E-03+4.1%−4.0%

2.22E-03+8.0%−8.0%

3.80E-01+3.1%−3.1%

5.17E-02+3.1%−3.1%

5.88E-03+3.0%−3.0%

134.5 7.18E-02+9.4%−9.2%

2.14E-03+4.0%−3.9%

2.25E-03+8.0%−7.9%

3.90E-01+3.1%−3.0%

5.32E-02+3.1%−3.0%

6.03E-03+3.0%−3.0%

135.0 7.08E-02+9.3%−9.2%

2.13E-03+4.0%−3.9%

2.27E-03+7.9%−7.9%

4.00E-01+3.0%−3.0%

5.47E-02+3.0%−3.0%

6.18E-03+2.9%−2.9%

135.5 6.97E-02+9.2%−9.1%

2.11E-03+3.8%−3.8%

2.30E-03+7.8%−7.8%

4.10E-01+2.9%−2.8%

5.62E-02+2.9%−2.8%

6.34E-03+2.8%−2.8%

136.0 6.87E-02+9.1%−9.0%

2.09E-03+3.7%−3.6%

2.32E-03+7.7%−7.7%

4.20E-01+2.8%−2.7%

5.77E-02+2.8%−2.7%

6.51E-03+2.7%−2.7%

136.5 6.76E-02+9.0%−8.9%

2.08E-03+3.6%−3.5%

2.34E-03+7.5%−7.5%

4.30E-01+2.6%−2.6%

5.91E-02+2.6%−2.6%

6.69E-03+2.6%−2.6%

137.0 6.65E-02+8.9%−8.8%

2.06E-03+3.5%−3.4%

2.36E-03+7.4%−7.4%

4.41E-01+2.5%−2.5%

6.06E-02+2.5%−2.5%

6.87E-03+2.5%−2.5%

137.5 6.54E-02+8.8%−8.7%

2.04E-03+3.3%−3.3%

2.38E-03+7.3%−7.3%

4.51E-01+2.4%−2.3%

6.20E-02+2.4%−2.3%

7.06E-03+2.3%−2.3%

138.0 6.43E-02+8.7%−8.5%

2.02E-03+3.2%−3.2%

2.40E-03+7.2%−7.2%

4.61E-01+2.2%−2.2%

6.34E-02+2.2%−2.2%

7.27E-03+2.2%−2.2%

138.5 6.32E-02+8.6%−8.4%

2.00E-03+3.1%−3.1%

2.42E-03+7.1%−7.1%

4.71E-01+2.1%−2.1%

6.48E-02+2.1%−2.1%

7.48E-03+2.1%−2.1%

139.0 6.20E-02+8.5%−8.3%

1.98E-03+3.0%−3.0%

2.43E-03+6.9%−7.0%

4.81E-01+1.9%−1.9%

6.61E-02+2.0%−1.9%

7.70E-03+2.0%−2.0%

139.5 6.08E-02+8.4%−8.2%

1.95E-03+2.9%−2.9%

2.45E-03+6.8%−6.8%

4.91E-01+1.8%−1.8%

6.75E-02+1.8%−1.8%

7.93E-03+1.9%−1.9%

140.0 5.97E-02+8.3%−8.1%

1.93E-03+2.7%−2.8%

2.46E-03+6.7%−6.7%

5.01E-01+1.7%−1.7%

6.87E-02+1.7%−1.7%

8.18E-03+1.8%−1.7%

141.0 5.72E-02+8.2%−8.1%

1.88E-03+2.7%−2.7%

2.48E-03+6.6%−6.7%

5.21E-01+1.6%−1.6%

7.12E-02+1.6%−1.6%

8.70E-03+1.7%−1.7%

142.0 5.48E-02+8.2%−8.1%

1.84E-03+2.6%−2.6%

2.49E-03+6.6%−6.6%

5.41E-01+1.5%−1.5%

7.35E-02+1.5%−1.5%

9.28E-03+1.6%−1.6%

143.0 5.23E-02+8.2%−8.0%

1.77E-03+2.5%−2.5%

2.49E-03+6.5%−6.5%

5.61E-01+1.4%−1.4%

7.56E-02+1.4%−1.4%

9.93E-03+1.6%−1.5%

144.0 4.99E-02+8.1%−8.0%

1.73E-03+2.5%−2.4%

2.49E-03+6.5%−6.5%

5.80E-01+1.3%−1.3%

7.75E-02+1.3%−1.3%

1.07E-02+1.5%−1.5%

145.0 4.74E-02+8.1%−8.0%

1.68E-03+2.4%−2.4%

2.48E-03+6.4%−6.4%

6.00E-01+1.2%−1.3%

7.91E-02+1.2%−1.3%

1.15E-02+1.4%−1.4%

146.0 4.48E-02+8.1%−7.9%

1.62E-03+2.4%−2.3%

2.46E-03+6.3%−6.3%

6.19E-01+1.2%−1.2%

8.05E-02+1.2%−1.2%

1.23E-02+1.4%−1.3%

147.0 4.22E-02+8.0%−7.9%

1.56E-03+2.3%−2.2%

2.44E-03+6.3%−6.3%

6.39E-01+1.1%−1.1%

8.16E-02+1.1%−1.1%

1.34E-02+1.3%−1.3%

148.0 3.96E-02+8.0%−7.9%

1.49E-03+2.2%−2.2%

2.39E-03+6.2%−6.3%

6.58E-01+1.0%−1.0%

8.24E-02+1.0%−1.0%

1.45E-02+1.2%−1.2%

149.0 3.72E-02+8.0%−7.9%

1.43E-03+2.2%−2.1%

2.36E-03+6.1%−6.2%

6.77E-01+0.9%−0.9%

8.26E-02+0.9%−0.9%

1.58E-02+1.2%−1.2%

150.0 3.46E-02+7.9%−7.8%

1.37E-03+2.1%−2.1%

2.31E-03+6.0%−6.2%

6.96E-01+0.9%−0.8%

8.25E-02+0.9%−0.8%

1.73E-02+1.1%−1.1%

151.0 3.20E-02+7.9%−7.8%

1.29E-03+2.1%−2.0%

2.24E-03+6.0%−6.1%

7.16E-01+0.8%−0.8%

8.19E-02+0.8%−0.8%

1.91E-02+1.1%−1.1%

152.0 2.95E-02+7.9%−7.8%

1.22E-03+2.0%−2.0%

2.19E-03+6.0%−6.0%

7.35E-01+0.7%−0.7%

8.08E-02+0.7%−0.7%

2.11E-02+1.0%−1.0%

153.0 2.69E-02+7.9%−7.8%

1.15E-03+2.0%−1.9%

2.11E-03+6.0%−6.0%

7.54E-01+0.7%−0.7%

7.90E-02+0.7%−0.7%

2.36E-02+1.0%−1.0%

154.0 2.44E-02+7.9%−7.7%

1.07E-03+1.9%−1.9%

2.02E-03+5.9%−5.9%

7.74E-01+0.6%−0.6%

7.66E-02+0.6%−0.6%

2.66E-02+0.9%−0.9%

155.0 2.18E-02+7.8%−7.7%

9.98E-04+1.9%−1.9%

1.91E-03+5.9%−5.8%

7.94E-01+0.5%−0.5%

7.34E-02+0.5%−0.5%

3.03E-02+0.9%−0.9%

156.0 1.92E-02+7.8%−7.7%

9.14E-04+1.8%−1.8%

1.79E-03+5.8%−5.8%

8.15E-01+0.5%−0.5%

6.92E-02+0.5%−0.5%

3.51E-02+0.8%−0.8%

157.0 1.65E-02+7.8%−7.7%

8.23E-04+1.8%−1.8%

1.65E-03+5.8%−5.8%

8.37E-01+0.4%−0.4%

6.40E-02+0.4%−0.4%

4.14E-02+0.8%−0.8%

158.0 1.39E-02+7.8%−7.7%

7.29E-04+1.7%−1.7%

1.50E-03+5.7%−5.7%

8.60E-01+0.3%−0.3%

5.76E-02+0.3%−0.3%

5.02E-02+0.7%−0.7%

159.0 1.12E-02+7.8%−7.7%

6.28E-04+1.7%−1.7%

1.33E-03+5.7%−5.7%

8.84E-01+0.3%−0.3%

4.99E-02+0.3%−0.3%

6.32E-02+0.7%−0.7%

160.0 8.65E-03+7.8%−7.7%

5.32E-04+1.6%−1.6%

1.16E-03+5.6%−5.7%

9.08E-01+0.2%−0.2%

4.15E-02+0.2%−0.2%

8.31E-02+0.6%−0.6%

162.0 5.04E-03+7.7%−7.7%

3.70E-04+1.6%−1.6%

8.41E-04+5.6%−5.6%

9.43E-01+0.2%−0.2%

2.82E-02+0.2%−0.2%

1.47E-01+0.6%−0.6%

164.0 3.54E-03+7.7%−7.7%

2.60E-04+1.6%−1.6%

6.06E-04+5.6%−5.6%

9.57E-01+0.1%−0.1%

2.31E-02+0.2%−0.2%

2.15E-01+0.6%−0.6%

166.0 2.85E-03+7.7%−7.7%

2.08E-04+1.6%−1.6%

5.00E-04+5.6%−5.6%

9.62E-01+0.1%−0.1%

2.18E-02+0.1%−0.1%

2.76E-01+0.6%−0.6%

168.0 2.46E-03+7.7%−7.7%

1.79E-04+1.6%−1.6%

4.40E-04+5.6%−5.6%

9.64E-01+0.1%−0.1%

2.22E-02+0.1%−0.1%

3.30E-01+0.6%−0.6%

170.0 2.20E-03+7.7%−7.7%

1.58E-04+1.6%−1.6%

4.00E-04+5.6%−5.6%

9.64E-01+0.1%−0.1%

2.36E-02+0.1%−0.1%

3.80E-01+0.6%−0.6%

November 18, 2011 – 11 : 26 DRAFT 20

Table 12: SM Higgs branching ratios to two gauge bosons and Higgs totalwidth together with their total uncer-tainties (expressed in percentage). Intermediate mass range.


172.0 2.01E-03+7.7%−7.6%

1.43E-04+1.6%−1.6%

3.70E-04+5.6%−5.6%

9.63E-01+0.0%−0.0%

2.61E-02+0.1%−0.1%

4.29E-01+0.6%−0.6%

174.0 1.88E-03+7.7%−7.6%

1.32E-04+1.6%−1.6%

3.48E-04+5.6%−5.5%

9.60E-01+0.0%−0.0%

2.98E-02+0.1%−0.1%

4.77E-01+0.6%−0.6%

176.0 1.76E-03+7.7%−7.6%

1.22E-04+1.6%−1.6%

3.29E-04+5.6%−5.5%

9.55E-01+0.0%−0.0%

3.54E-02+0.1%−0.1%

5.25E-01+0.6%−0.6%

178.0 1.65E-03+7.7%−7.6%

1.14E-04+1.6%−1.6%

3.12E-04+5.6%−5.5%

9.47E-01+0.0%−0.0%

4.44E-02+0.1%−0.1%

5.75E-01+0.6%−0.6%

180.0 1.56E-03+7.7%−7.6%

1.05E-04+1.6%−1.6%

2.96E-04+5.6%−5.5%

9.32E-01+0.0%−0.0%

6.02E-02+0.1%−0.1%

6.31E-01+0.6%−0.6%

182.0 1.44E-03+7.7%−7.6%

9.69E-05+1.6%−1.6%

2.76E-04+5.6%−5.5%

9.03E-01+0.0%−0.0%

9.00E-02+0.1%−0.1%

7.00E-01+0.6%−0.6%

184.0 1.32E-03+7.7%−7.6%

8.81E-05+1.6%−1.6%

2.54E-04+5.6%−5.5%

8.62E-01+0.0%−0.0%

1.31E-01+0.0%−0.0%

7.88E-01+0.6%−0.6%

186.0 1.23E-03+7.7%−7.6%

8.09E-05+1.6%−1.6%

2.35E-04+5.6%−5.5%

8.28E-01+0.0%−0.0%

1.66E-01+0.0%−0.0%

8.76E-01+0.5%−0.6%

188.0 1.16E-03+7.7%−7.6%

7.52E-05+1.6%−1.5%

2.22E-04+5.6%−5.5%

8.03E-01+0.0%−0.0%

1.91E-01+0.0%−0.0%

9.60E-01+0.5%−0.5%

190.0 1.10E-03+7.7%−7.6%

7.05E-05+1.6%−1.5%

2.11E-04+5.6%−5.5%

7.86E-01+0.0%−0.0%

2.09E-01+0.0%−0.0%

1.04E+00+0.5%−0.5%

192.0 1.05E-03+7.7%−7.6%

6.66E-05+1.6%−1.6%

2.02E-04+5.6%−5.5%

7.72E-01+0.0%−0.0%

2.23E-01+0.0%−0.0%

1.12E+00+0.5%−0.5%

194.0 1.01E-03+7.7%−7.6%

6.32E-05+1.6%−1.6%

1.94E-04+5.6%−5.5%

7.61E-01+0.0%−0.0%

2.34E-01+0.0%−0.0%

1.20E+00+0.5%−0.5%

196.0 9.79E-04+7.7%−7.6%

6.02E-05+1.6%−1.6%

1.87E-04+5.5%−5.6%

7.53E-01+0.0%−0.0%

2.43E-01+0.0%−0.0%

1.28E+00+0.5%−0.5%

198.0 9.51E-04+7.6%−7.6%

5.75E-05+1.6%−1.6%

1.81E-04+5.5%−5.6%

7.46E-01+0.0%−0.0%

2.50E-01+0.0%−0.0%

1.35E+00+0.5%−0.5%

200.0 9.26E-04+7.6%−7.6%

5.51E-05+1.6%−1.6%

1.75E-04+5.5%−5.6%

7.41E-01+0.0%−0.0%

2.55E-01+0.0%−0.0%

1.43E+00+0.5%−0.5%

202.0 9.04E-04+7.6%−7.5%

5.28E-05+1.6%−1.6%

1.70E-04+5.5%−5.6%

7.36E-01+0.0%−0.0%

2.60E-01+0.0%−0.0%

1.51E+00+0.5%−0.5%

204.0 8.84E-04+7.6%−7.5%

5.08E-05+1.6%−1.6%

1.65E-04+5.6%−5.6%

7.32E-01+0.0%−0.0%

2.65E-01+0.0%−0.0%

1.59E+00+0.5%−0.5%

206.0 8.66E-04+7.6%−7.5%

4.89E-05+1.6%−1.6%

1.61E-04+5.6%−5.6%

7.28E-01+0.0%−0.0%

2.68E-01+0.0%−0.0%

1.68E+00+0.5%−0.5%

208.0 8.51E-04+7.6%−7.5%

4.71E-05+1.6%−1.6%

1.57E-04+5.6%−5.6%

7.25E-01+0.0%−0.0%

2.71E-01+0.0%−0.0%

1.76E+00+0.5%−0.5%

210.0 8.36E-04+7.6%−7.5%

4.55E-05+1.7%−1.6%

1.53E-04+5.6%−5.5%

7.23E-01+0.0%−0.0%

2.74E-01+0.0%−0.0%

1.85E+00+0.5%−0.5%

212.0 8.22E-04+7.6%−7.5%

4.39E-05+1.6%−1.6%

1.49E-04+5.6%−5.5%

7.20E-01+0.0%−0.0%

2.76E-01+0.0%−0.0%

1.93E+00+0.5%−0.5%

214.0 8.09E-04+7.6%−7.5%

4.24E-05+1.6%−1.6%

1.45E-04+5.6%−5.5%

7.18E-01+0.0%−0.0%

2.78E-01+0.0%−0.0%

2.02E+00+0.5%−0.5%

216.0 7.98E-04+7.6%−7.5%

4.10E-05+1.6%−1.6%

1.41E-04+5.6%−5.6%

7.17E-01+0.0%−0.0%

2.80E-01+0.0%−0.0%

2.12E+00+0.5%−0.5%

218.0 7.87E-04+7.6%−7.5%

3.96E-05+1.6%−1.6%

1.38E-04+5.6%−5.6%

7.15E-01+0.0%−0.0%

2.82E-01+0.0%−0.0%

2.21E+00+0.5%−0.5%

220.0 7.77E-04+7.6%−7.5%

3.83E-05+1.6%−1.6%

1.35E-04+5.6%−5.6%

7.14E-01+0.0%−0.0%

2.84E-01+0.0%−0.0%

2.31E+00+0.5%−0.5%

222.0 7.67E-04+7.6%−7.5%

3.72E-05+1.6%−1.6%

1.31E-04+5.6%−5.5%

7.12E-01+0.0%−0.0%

2.85E-01+0.0%−0.0%

2.40E+00+0.5%−0.5%

224.0 7.59E-04+7.6%−7.5%

3.60E-05+1.6%−1.6%

1.28E-04+5.6%−5.5%

7.11E-01+0.0%−0.0%

2.86E-01+0.0%−0.0%

2.50E+00+0.5%−0.5%

226.0 7.51E-04+7.6%−7.5%

3.49E-05+1.6%−1.6%

1.25E-04+5.6%−5.5%

7.10E-01+0.0%−0.0%

2.87E-01+0.0%−0.0%

2.61E+00+0.5%−0.5%

228.0 7.43E-04+7.6%−7.5%

3.39E-05+1.6%−1.6%

1.22E-04+5.6%−5.5%

7.09E-01+0.0%−0.0%

2.88E-01+0.0%−0.0%

2.71E+00+0.5%−0.5%

230.0 7.35E-04+7.6%−7.5%

3.28E-05+1.6%−1.6%

1.19E-04+5.6%−5.5%

7.08E-01+0.0%−0.0%

2.89E-01+0.0%−0.0%

2.82E+00+0.5%−0.5%

232.0 7.28E-04+7.6%−7.5%

3.19E-05+1.6%−1.6%

1.17E-04+5.6%−5.5%

7.07E-01+0.0%−0.0%

2.90E-01+0.0%−0.0%

2.93E+00+0.5%−0.5%

234.0 7.22E-04+7.6%−7.5%

3.09E-05+1.6%−1.6%

1.14E-04+5.6%−5.5%

7.06E-01+0.0%−0.0%

2.91E-01+0.0%−0.0%

3.04E+00+0.5%−0.5%

236.0 7.16E-04+7.6%−7.5%

3.00E-05+1.6%−1.6%

1.11E-04+5.5%−5.6%

7.06E-01+0.0%−0.0%

2.92E-01+0.0%−0.0%

3.16E+00+0.5%−0.5%

238.0 7.11E-04+7.6%−7.5%

2.92E-05+1.6%−1.6%

1.09E-04+5.5%−5.6%

7.05E-01+0.0%−0.0%

2.93E-01+0.0%−0.0%

3.27E+00+0.5%−0.5%

240.0 7.05E-04+7.6%−7.5%

2.84E-05+1.7%−1.6%

1.06E-04+5.5%−5.6%

7.04E-01+0.0%−0.0%

2.94E-01+0.0%−0.0%

3.40E+00+0.5%−0.5%

242.0 7.00E-04+7.6%−7.5%

2.76E-05+1.7%−1.6%

1.04E-04+5.5%−5.6%

7.04E-01+0.0%−0.0%

2.94E-01+0.0%−0.0%

3.52E+00+0.5%−0.5%

244.0 6.95E-04+7.6%−7.5%

2.68E-05+1.7%−1.7%

1.02E-04+5.5%−5.6%

7.03E-01+0.0%−0.0%

2.95E-01+0.0%−0.0%

3.64E+00+0.5%−0.5%

246.0 6.90E-04+7.6%−7.5%

2.61E-05+1.7%−1.7%

9.96E-05+5.5%−5.6%

7.02E-01+0.0%−0.0%

2.96E-01+0.0%−0.0%

3.77E+00+0.5%−0.5%

248.0 6.86E-04+7.6%−7.5%

2.54E-05+1.7%−1.7%

9.75E-05+5.6%−5.6%

7.02E-01+0.0%−0.0%

2.96E-01+0.0%−0.0%

3.91E+00+0.5%−0.5%

250.0 6.82E-04+7.6%−7.5%

2.47E-05+1.7%−1.7%

9.54E-05+5.6%−5.6%

7.01E-01+0.0%−0.0%

2.97E-01+0.0%−0.0%

4.04E+00+0.5%−0.5%

252.0 6.78E-04+7.6%−7.5%

2.40E-05+1.7%−1.7%

9.34E-05+5.6%−5.6%

7.01E-01+0.0%−0.0%

2.97E-01+0.0%−0.0%

4.18E+00+0.5%−0.5%

254.0 6.75E-04+7.6%−7.5%

2.34E-05+1.7%−1.7%

9.14E-05+5.6%−5.6%

7.00E-01+0.0%−0.0%

2.98E-01+0.0%−0.0%

4.32E+00+0.5%−0.5%

256.0 6.72E-04+7.6%−7.5%

2.29E-05+1.7%−1.7%

8.94E-05+5.6%−5.6%

7.00E-01+0.0%−0.0%

2.98E-01+0.0%−0.0%

4.46E+00+0.5%−0.5%

258.0 6.69E-04+7.6%−7.5%

2.23E-05+1.7%−1.7%

8.75E-05+5.6%−5.6%

6.99E-01+0.0%−0.0%

2.99E-01+0.0%−0.0%

4.61E+00+0.5%−0.5%

260.0 6.66E-04+7.7%−7.5%

2.17E-05+1.7%−1.7%

8.57E-05+5.6%−5.6%

6.99E-01+0.0%−0.0%

2.99E-01+0.0%−0.0%

4.76E+00+0.5%−0.5%

November 18, 2011 – 11 : 26 DRAFT 21

Table 13: SM Higgs branching ratios to two gauge bosons and Higgs totalwidth together with their total uncer-tainties (expressed in percentage). High mass range.


262.0 6.64E-04+7.7%−7.5%

2.11E-05+1.7%−1.7%

8.39E-05+5.6%−5.6%

6.98E-01+0.0%−0.0%

3.00E-01+0.0%−0.0%

4.91E+00+0.5%−0.5%

264.0 6.61E-04+7.7%−7.5%

2.06E-05+1.7%−1.7%

8.21E-05+5.6%−5.6%

6.98E-01+0.0%−0.0%

3.00E-01+0.0%−0.0%

5.07E+00+0.5%−0.5%

266.0 6.59E-04+7.7%−7.6%

2.01E-05+1.7%−1.7%

8.04E-05+5.6%−5.6%

6.98E-01+0.0%−0.0%

3.01E-01+0.0%−0.0%

5.23E+00+0.5%−0.5%

268.0 6.57E-04+7.7%−7.6%

1.96E-05+1.7%−1.7%

7.88E-05+5.6%−5.6%

6.97E-01+0.0%−0.0%

3.01E-01+0.0%−0.0%

5.39E+00+0.5%−0.5%

270.0 6.55E-04+7.7%−7.6%

1.91E-05+1.7%−1.7%

7.72E-05+5.6%−5.6%

6.97E-01+0.0%−0.0%

3.02E-01+0.0%−0.0%

5.55E+00+0.5%−0.5%

272.0 6.54E-04+7.7%−7.6%

1.87E-05+1.7%−1.7%

7.56E-05+5.6%−5.6%

6.96E-01+0.0%−0.0%

3.02E-01+0.0%−0.0%

5.72E+00+0.5%−0.5%

274.0 6.53E-04+7.7%−7.6%

1.82E-05+1.7%−1.7%

7.41E-05+5.6%−5.6%

6.96E-01+0.0%−0.0%

3.02E-01+0.0%−0.0%

5.89E+00+0.5%−0.5%

276.0 6.51E-04+7.7%−7.6%

1.78E-05+1.8%−1.7%

7.26E-05+5.6%−5.6%

6.96E-01+0.0%−0.0%

3.03E-01+0.0%−0.0%

6.07E+00+0.5%−0.5%

278.0 6.51E-04+7.7%−7.6%

1.74E-05+1.8%−1.7%

7.12E-05+5.6%−5.6%

6.95E-01+0.0%−0.0%

3.03E-01+0.0%−0.0%

6.25E+00+0.5%−0.5%

280.0 6.50E-04+7.7%−7.6%

1.68E-05+1.8%−1.8%

6.98E-05+5.6%−5.6%

6.95E-01+0.0%−0.0%

3.04E-01+0.0%−0.0%

6.43E+00+0.5%−0.5%

282.0 6.49E-04+7.8%−7.6%

1.65E-05+1.8%−1.8%

6.84E-05+5.6%−5.6%

6.95E-01+0.0%−0.0%

3.04E-01+0.0%−0.0%

6.61E+00+0.5%−0.5%

284.0 6.49E-04+7.8%−7.7%

1.61E-05+1.8%−1.8%

6.71E-05+5.6%−5.6%

6.94E-01+0.0%−0.0%

3.04E-01+0.0%−0.0%

6.80E+00+0.5%−0.5%

286.0 6.49E-04+7.8%−7.7%

1.57E-05+1.8%−1.8%

6.58E-05+5.6%−5.6%

6.94E-01+0.0%−0.0%

3.05E-01+0.0%−0.0%

6.99E+00+0.5%−0.5%

288.0 6.49E-04+7.8%−7.7%

1.53E-05+1.8%−1.8%

6.45E-05+5.6%−5.6%

6.93E-01+0.0%−0.0%

3.05E-01+0.0%−0.0%

7.19E+00+0.5%−0.5%

290.0 6.49E-04+7.9%−7.7%

1.50E-05+1.8%−1.8%

6.32E-05+5.6%−5.6%

6.93E-01+0.0%−0.0%

3.05E-01+0.0%−0.0%

7.39E+00+0.5%−0.5%

295.0 6.51E-04+7.9%−7.8%

1.42E-05+1.8%−1.8%

6.03E-05+5.6%−5.6%

6.92E-01+0.0%−0.0%

3.06E-01+0.0%−0.0%

7.90E+00+0.5%−0.5%

300.0 6.54E-04+8.0%−7.8%

1.34E-05+1.8%−1.8%

5.75E-05+5.6%−5.6%

6.92E-01+0.0%−0.0%

3.07E-01+0.0%−0.0%

8.43E+00+0.5%−0.5%

305.0 6.58E-04+8.1%−7.9%

1.27E-05+1.8%−1.8%

5.49E-05+5.6%−5.6%

6.91E-01+0.0%−0.0%

3.08E-01+0.0%−0.0%

8.99E+00+0.5%−0.5%

310.0 6.64E-04+8.2%−8.0%

1.20E-05+1.9%−1.9%

5.23E-05+5.6%−5.6%

6.90E-01+0.0%−0.0%

3.08E-01+0.0%−0.0%

9.57E+00+0.5%−0.5%

315.0 6.71E-04+8.4%−8.1%

1.14E-05+1.9%−1.9%

5.00E-05+5.6%−5.6%

6.90E-01+0.0%−0.0%

3.09E-01+0.0%−0.0%

1.02E+01+0.5%−0.5%

320.0 6.80E-04+8.6%−8.2%

1.09E-05+1.9%−1.9%

4.79E-05+5.7%−5.5%

6.89E-01+0.0%−0.0%

3.09E-01+0.0%−0.0%

1.08E+01+0.5%−0.5%

325.0 6.92E-04+8.9%−8.4%

1.03E-05+1.9%−1.9%

4.58E-05+5.7%−5.5%

6.88E-01+0.0%−0.0%

3.10E-01+0.1%−0.1%

1.14E+01+0.5%−0.6%

330.0 7.07E-04+9.1%−8.6%

9.83E-06+1.9%−2.0%

4.39E-05+5.6%−5.5%

6.88E-01+0.0%−0.0%

3.10E-01+0.1%−0.1%

1.21E+01+0.5%−0.6%

335.0 7.26E-04+10.0%−9.0%

9.37E-06+2.0%−2.2%

4.21E-05+5.6%−5.5%

6.87E-01+0.0%−0.1%

3.11E-01+0.1%−0.2%

1.28E+01+0.6%−0.7%

340.0 7.51E-04+10.8%−9.4%

8.92E-06+2.1%−2.5%

4.03E-05+5.6%−5.5%

6.87E-01+0.0%−0.2%

3.11E-01+0.1%−0.3%

1.35E+01+0.7%−0.7%

345.0 7.83E-04+10.1%−9.9%

8.44E-06+4.1%−5.2%

3.88E-05+6.7%−7.1%

6.85E-01+0.7%−1.1%

3.11E-01+0.8%−1.2%

1.42E+01+1.8%−1.4%

350.0 8.14E-04+9.5%−10.5%

7.73E-06+6.1%−7.9%

3.65E-05+7.7%−8.6%

6.76E-01+1.4%−2.0%

3.07E-01+1.5%−2.1%

1.52E+01+2.9%−2.1%

360.0 8.51E-04+8.6%−8.4%

6.25E-06+9.4%−8.7%

3.18E-05+9.5%−8.8%

6.51E-01+2.6%−2.3%

2.97E-01+2.7%−2.3%

1.76E+01+2.9%−3.4%

370.0 8.64E-04+8.4%−7.7%

5.04E-06+10.4%−9.0%

2.77E-05+9.8%−8.7%

6.28E-01+2.9%−2.3%

2.87E-01+2.9%−2.3%

2.02E+01+2.7%−3.7%

380.0 8.61E-04+8.5%−7.5%

4.06E-06+10.9%−9.4%

2.43E-05+9.9%−8.6%

6.09E-01+3.1%−2.3%

2.80E-01+3.0%−2.3%

2.31E+01+2.6%−3.7%

390.0 8.50E-04+8.7%−7.5%

3.28E-06+11.3%−9.5%

2.14E-05+9.9%−8.5%

5.94E-01+3.1%−2.2%

2.74E-01+3.1%−2.2%

2.61E+01+2.5%−3.7%

400.0 8.32E-04+8.9%−7.6%

2.65E-06+11.5%−9.7%

1.90E-05+9.9%−8.4%

5.82E-01+3.1%−2.1%

2.69E-01+3.1%−2.1%

2.92E+01+2.3%−3.6%

410.0 8.11E-04+9.1%−7.7%

2.15E-06+11.8%−9.7%

1.70E-05+9.8%−8.2%

5.72E-01+3.1%−2.0%

2.66E-01+3.0%−2.0%

3.25E+01+2.2%−3.6%

420.0 7.89E-04+9.2%−7.8%

1.74E-06+11.9%−9.7%

1.53E-05+9.6%−8.1%

5.65E-01+3.1%−1.9%

2.63E-01+3.0%−1.9%

3.59E+01+2.1%−3.5%

430.0 7.65E-04+9.3%−7.9%

1.41E-06+12.2%−9.9%

1.39E-05+9.5%−8.0%

5.59E-01+3.0%−1.9%

2.61E-01+3.0%−1.8%

3.94E+01+1.9%−3.4%

440.0 7.41E-04+9.4%−8.0%

1.15E-06+12.1%−10.0%

1.26E-05+9.4%−7.8%

5.55E-01+3.0%−1.8%

2.60E-01+2.9%−1.7%

4.30E+01+1.8%−3.3%

450.0 7.18E-04+9.5%−8.0%

9.28E-07+12.3%−10.0%

1.15E-05+9.2%−7.6%

5.51E-01+2.9%−1.7%

2.59E-01+2.8%−1.6%

4.68E+01+1.7%−3.2%

460.0 6.94E-04+9.6%−8.1%

7.51E-07+12.2%−10.0%

1.05E-05+9.1%−7.4%

5.49E-01+2.8%−1.6%

2.59E-01+2.8%−1.6%

5.08E+01+1.6%−3.1%

470.0 6.71E-04+9.6%−8.1%

6.05E-07+12.5%−9.7%

9.64E-06+9.0%−7.4%

5.47E-01+2.8%−1.6%

2.59E-01+2.7%−1.5%

5.49E+01+1.6%−3.1%

480.0 6.48E-04+9.7%−8.1%

4.87E-07+12.4%−9.6%

8.88E-06+8.8%−7.2%

5.46E-01+2.7%−1.5%

2.60E-01+2.6%−1.4%

5.91E+01+1.5%−3.0%

490.0 6.26E-04+9.7%−8.2%

3.90E-07+12.1%−9.4%

8.19E-06+8.7%−7.1%

5.46E-01+2.6%−1.4%

2.60E-01+2.6%−1.4%

6.35E+01+1.4%−2.9%

500.0 6.04E-04+9.9%−7.9%

3.12E-07+11.9%−8.7%

7.58E-06+8.7%−6.7%

5.46E-01+2.4%−1.1%

2.61E-01+2.3%−1.1%

6.80E+01+1.1%−3.0%

510.0 5.83E-04+9.9%−8.0%

2.47E-07+11.6%−8.0%

7.03E-06+8.7%−6.6%

5.46E-01+2.3%−1.1%

2.62E-01+2.4%−1.1%

7.27E+01+1.1%−3.0%

520.0 5.62E-04+10.1%−8.0%

1.96E-07+10.9%−7.2%

6.53E-06+8.6%−6.5%

5.47E-01+2.4%−1.1%

2.63E-01+2.4%−1.2%

7.75E+01+1.2%−3.1%

530.0 5.42E-04+10.1%−8.2%

1.56E-07+9.8%−5.9%

6.08E-06+8.6%−6.5%

5.48E-01+2.4%−1.1%

2.64E-01+2.4%−1.2%

8.25E+01+1.3%−3.3%

540.0 5.24E-04+10.2%−8.3%

1.24E-07+8.3%−4.2%

5.67E-06+8.6%−6.5%

5.49E-01+2.4%−1.2%

2.65E-01+2.5%−1.2%

8.77E+01+1.5%−3.4%

November 18, 2011 – 11 : 26 DRAFT 22

Table 14: SM Higgs branching ratios to two gauge bosons and Higgs totalwidth together with their total uncer-tainties (expressed in percentage). Very high mass range.


550.0 5.05E-04+10.4%−8.4%

9.90E-08+6.1%−2.7%

5.30E-06+8.6%−6.6%

5.50E-01+2.4%−1.2%

2.66E-01+2.5%−1.2%

9.30E+01+1.6%−3.5%

560.0 4.88E-04+10.5%−8.6%

8.10E-08+8.7%−3.2%

4.95E-06+8.6%−6.6%

5.52E-01+2.5%−1.2%

2.67E-01+2.5%−1.2%

9.86E+01+1.7%−3.6%

570.0 4.71E-04+10.6%−8.7%

6.83E-08+11.5%−7.2%

4.64E-06+8.6%−6.7%

5.53E-01+2.5%−1.2%

2.68E-01+2.5%−1.3%

1.04E+02+1.9%−3.7%

580.0 4.55E-04+10.7%−8.9%

5.91E-08+15.2%−10.3%

4.35E-06+8.7%−6.9%

5.55E-01+2.5%−1.2%

2.70E-01+2.5%−1.3%

1.10E+02+2.0%−3.8%

590.0 4.39E-04+10.9%−8.9%

5.33E-08+17.8%−13.5%

4.08E-06+8.9%−6.9%

5.57E-01+2.5%−1.3%

2.71E-01+2.5%−1.3%

1.16E+02+2.2%−3.9%

600.0 4.24E-04+11.1%−9.1%

5.03E-08+20.7%−16.0%

3.84E-06+9.2%−7.1%

5.58E-01+2.5%−1.3%

2.72E-01+2.5%−1.3%

1.23E+02+2.3%−4.0%

610.0 4.10E-04+11.0%−9.3%

4.86E-08+22.0%−17.2%

3.61E-06+9.3%−7.5%

5.60E-01+2.5%−1.3%

2.74E-01+2.6%−1.3%

1.29E+02+2.5%−4.2%

620.0 3.96E-04+11.2%−9.4%

4.82E-08+24.2%−19.1%

3.40E-06+9.4%−7.6%

5.62E-01+2.6%−1.3%

2.75E-01+2.6%−1.3%

1.36E+02+2.6%−4.3%

630.0 3.82E-04+11.4%−9.5%

4.93E-08+27.1%−20.8%

3.21E-06+9.7%−7.8%

5.64E-01+2.5%−1.3%

2.76E-01+2.6%−1.3%

1.43E+02+2.8%−4.5%

640.0 3.69E-04+11.6%−9.8%

5.29E-08+28.1%−22.8%

3.03E-06+9.9%−8.1%

5.66E-01+2.6%−1.3%

2.77E-01+2.6%−1.3%

1.50E+02+3.0%−4.6%

650.0 3.57E-04+11.8%−9.9%

5.82E-08+28.0%−23.9%

2.86E-06+10.1%−8.3%

5.68E-01+2.6%−1.3%

2.79E-01+2.6%−1.3%

1.58E+02+3.1%−4.8%

660.0 3.45E-04+11.9%−10.2%

6.60E-08+27.1%−23.1%

2.70E-06+10.3%−8.5%

5.70E-01+2.6%−1.3%

2.80E-01+2.6%−1.3%

1.65E+02+3.3%−4.9%

670.0 3.33E-04+12.1%−10.3%

7.56E-08+25.1%−21.7%

2.56E-06+10.6%−8.7%

5.71E-01+2.6%−1.3%

2.81E-01+2.6%−1.3%

1.73E+02+3.5%−5.1%

680.0 3.22E-04+12.4%−10.5%

8.65E-08+22.7%−20.2%

2.42E-06+10.8%−8.9%

5.73E-01+2.6%−1.3%

2.82E-01+2.6%−1.3%

1.82E+02+3.7%−5.3%

690.0 3.12E-04+12.5%−10.8%

9.86E-08+21.2%−18.5%

2.30E-06+11.1%−9.2%

5.75E-01+2.6%−1.3%

2.84E-01+2.6%−1.3%

1.90E+02+3.9%−5.5%

700.0 3.01E-04+12.7%−11.0%

1.11E-07+20.1%−17.1%

2.18E-06+11.4%−9.5%

5.77E-01+2.6%−1.3%

2.85E-01+2.6%−1.3%

1.99E+02+4.1%−5.6%

710.0 2.91E-04+13.0%−11.2%

1.24E-07+18.8%−16.0%

2.07E-06+11.6%−9.8%

5.79E-01+2.6%−1.3%

2.86E-01+2.6%−1.3%

2.08E+02+4.3%−5.9%

720.0 2.81E-04+13.3%−11.5%

1.38E-07+17.6%−15.3%

1.96E-06+12.0%−10.0%

5.81E-01+2.6%−1.3%

2.87E-01+2.6%−1.3%

2.17E+02+4.6%−6.1%

730.0 2.73E-04+13.6%−11.7%

1.52E-07+17.0%−14.4%

1.87E-06+12.2%−10.3%

5.83E-01+2.6%−1.3%

2.88E-01+2.6%−1.3%

2.27E+02+4.8%−6.3%

740.0 2.63E-04+13.9%−11.9%

1.65E-07+16.4%−14.0%

1.77E-06+12.5%−10.6%

5.84E-01+2.6%−1.3%

2.89E-01+2.6%−1.3%

2.37E+02+5.1%−6.5%

750.0 2.54E-04+14.1%−12.2%

1.79E-07+16.0%−13.6%

1.69E-06+12.9%−10.9%

5.86E-01+2.6%−1.3%

2.90E-01+2.6%−1.3%

2.47E+02+5.3%−6.8%

760.0 2.46E-04+14.4%−12.4%

1.92E-07+15.6%−13.2%

1.61E-06+13.2%−11.2%

5.88E-01+2.6%−1.3%

2.91E-01+2.6%−1.3%

2.58E+02+5.6%−7.0%

770.0 2.38E-04+14.7%−12.8%

2.05E-07+15.6%−13.0%

1.53E-06+13.6%−11.4%

5.89E-01+2.6%−1.3%

2.93E-01+2.6%−1.2%

2.69E+02+5.9%−7.3%

780.0 2.30E-04+15.1%−13.0%

2.18E-07+15.1%−12.9%

1.46E-06+13.9%−11.8%

5.91E-01+2.6%−1.3%

2.94E-01+2.6%−1.3%

2.80E+02+6.2%−7.6%

790.0 2.23E-04+15.5%−13.3%

2.31E-07+15.0%−12.7%

1.40E-06+14.4%−12.2%

5.93E-01+2.7%−1.3%

2.95E-01+2.6%−1.3%

2.92E+02+6.5%−7.9%

800.0 2.16E-04+15.8%−13.6%

2.44E-07+15.2%−12.7%

1.33E-06+14.8%−12.5%

5.94E-01+2.7%−1.3%

2.96E-01+2.7%−1.3%

3.04E+02+6.8%−8.2%

810.0 2.09E-04+16.3%−13.9%

2.57E-07+15.0%−12.7%

1.27E-06+15.1%−12.8%

5.96E-01+2.7%−1.3%

2.96E-01+2.7%−1.3%

3.17E+02+7.1%−8.6%

820.0 2.02E-04+16.8%−14.2%

2.69E-07+15.3%−12.6%

1.22E-06+15.6%−13.2%

5.98E-01+2.7%−1.4%

2.97E-01+2.7%−1.3%

3.30E+02+7.5%−8.9%

830.0 1.96E-04+17.1%−14.6%

2.82E-07+15.3%−12.6%

1.16E-06+16.2%−13.5%

5.99E-01+2.7%−1.4%

2.98E-01+2.7%−1.4%

3.43E+02+7.8%−9.2%

840.0 1.90E-04+17.6%−14.9%

2.93E-07+15.4%−12.8%

1.12E-06+16.6%−13.9%

6.01E-01+2.7%−1.4%

2.99E-01+2.7%−1.4%

3.57E+02+8.2%−9.6%

850.0 1.84E-04+18.1%−15.2%

3.03E-07+15.7%−12.8%

1.07E-06+17.1%−14.2%

6.02E-01+2.7%−1.4%

3.00E-01+2.7%−1.4%

3.71E+02+8.6%−10.0%

860.0 1.78E-04+18.6%−15.7%

3.15E-07+16.1%−12.9%

1.02E-06+17.6%−14.7%

6.04E-01+2.7%−1.4%

3.01E-01+2.7%−1.4%

3.86E+02+9.0%−10.4%

870.0 1.72E-04+19.1%−16.0%

3.27E-07+16.2%−13.2%

9.83E-07+18.1%−15.1%

6.05E-01+2.7%−1.4%

3.02E-01+2.7%−1.4%

4.01E+02+9.4%−10.8%

880.0 1.67E-04+19.7%−16.3%

3.38E-07+16.6%−13.3%

9.44E-07+18.7%−15.4%

6.06E-01+2.8%−1.5%

3.03E-01+2.7%−1.4%

4.16E+02+9.8%−11.3%

890.0 1.62E-04+20.2%−16.9%

3.48E-07+17.0%−13.5%

9.06E-07+19.3%−15.9%

6.08E-01+2.8%−1.5%

3.03E-01+2.7%−1.5%

4.32E+02+10.3%−11.7%

900.0 1.57E-04+20.9%−17.1%

3.58E-07+17.1%−13.8%

8.71E-07+19.9%−16.3%

6.09E-01+2.8%−1.5%

3.04E-01+2.8%−1.5%

4.49E+02+10.8%−12.2%

910.0 1.52E-04+21.4%−17.6%

3.67E-07+17.9%−13.8%

8.39E-07+20.6%−16.7%

6.10E-01+2.8%−1.5%

3.05E-01+2.8%−1.5%

4.66E+02+11.2%−12.7%

920.0 1.48E-04+22.1%−18.0%

3.77E-07+18.8%−14.1%

8.07E-07+21.2%−17.2%

6.12E-01+2.8%−1.5%

3.06E-01+2.8%−1.5%

4.84E+02+11.7%−13.2%

930.0 1.44E-04+22.8%−18.5%

3.86E-07+18.9%−15.0%

7.77E-07+21.9%−17.6%

6.13E-01+2.8%−1.6%

3.06E-01+2.8%−1.5%

5.02E+02+12.2%−13.7%

940.0 1.39E-04+23.4%−18.9%

3.93E-07+19.5%−15.0%

7.49E-07+22.7%−18.1%

6.14E-01+2.8%−1.6%

3.07E-01+2.8%−1.5%

5.21E+02+12.8%−14.2%

950.0 1.35E-04+24.3%−19.3%

4.00E-07+20.1%−15.3%

7.22E-07+23.4%−18.5%

6.16E-01+2.8%−1.6%

3.08E-01+2.8%−1.6%

5.40E+02+13.3%−14.8%

960.0 1.31E-04+25.1%−19.8%

4.09E-07+20.9%−15.6%

6.97E-07+24.3%−19.0%

6.17E-01+2.8%−1.6%

3.09E-01+2.8%−1.6%

5.60E+02+13.9%−15.3%

970.0 1.27E-04+25.8%−20.3%

4.17E-07+21.5%−16.0%

6.74E-07+25.1%−19.5%

6.18E-01+2.8%−1.6%

3.09E-01+2.8%−1.6%

5.81E+02+14.5%−15.9%

980.0 1.23E-04+26.8%−20.8%

4.26E-07+22.3%−16.3%

6.51E-07+26.0%−20.0%

6.19E-01+2.9%−1.6%

3.10E-01+2.8%−1.6%

6.02E+02+15.1%−16.6%

990.0 1.19E-04+27.7%−21.3%

4.33E-07+23.0%−16.8%

6.29E-07+26.9%−20.5%

6.20E-01+2.9%−1.6%

3.10E-01+2.8%−1.6%

6.24E+02+15.7%−17.2%

1000.0 1.16E-04+28.6%−21.8%

4.39E-07+24.0%−17.1%

6.08E-07+27.8%−21.0%

6.21E-01+2.9%−1.7%

3.11E-01+2.8%−1.6%

6.47E+02+16.3%−17.8%

November 18, 2011 – 11 : 26 DRAFT 23

Table 15: SM Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their total uncertain-ties (expressed in percentage). Very low mass range.

MH H → 4l H → 4l H → eeee H → eeµµ H → 2l2ν H → 2l2ν H → eνeν H → eνµν ∆BR

[ GeV] l = e, µ, τ l = e, µ l = e, µ, τ l = e, µ [%]

ν = any ν = any

90.0 4.89E-06 2.33E-06 7.01E-07 9.30E-07 2.10E-04 9.12E-05 1.75E-05 2.43E-05 ±5.8

95.0 7.73E-06 3.67E-06 1.10E-06 1.48E-06 4.80E-04 2.10E-04 4.42E-05 5.49E-05 ±5.8

100.0 1.28E-05 6.06E-06 1.78E-06 2.49E-06 1.14E-03 5.03E-04 1.13E-04 1.29E-04 ±5.7

105.0 2.37E-05 1.11E-05 3.18E-06 4.74E-06 2.53E-03 1.12E-03 2.59E-04 2.83E-04 ±5.6

110.0 4.72E-05 2.18E-05 6.04E-06 9.69E-06 5.08E-03 2.26E-03 5.32E-04 5.61E-04 ±5.4

110.5 5.06E-05 2.33E-05 6.45E-06 1.04E-05 5.41E-03 2.41E-03 5.68E-04 5.97E-04 ±5.4

111.0 5.42E-05 2.49E-05 6.88E-06 1.12E-05 5.76E-03 2.57E-03 6.06E-04 6.35E-04 ±5.4

111.5 5.80E-05 2.67E-05 7.34E-06 1.20E-05 6.13E-03 2.74E-03 6.45E-04 6.75E-04 ±5.4

112.0 6.21E-05 2.85E-05 7.82E-06 1.29E-05 6.52E-03 2.91E-03 6.87E-04 7.17E-04 ±5.3

112.5 6.64E-05 3.05E-05 8.34E-06 1.38E-05 6.92E-03 3.09E-03 7.31E-04 7.61E-04 ±5.3

113.0 7.10E-05 3.26E-05 8.88E-06 1.48E-05 7.35E-03 3.28E-03 7.76E-04 8.07E-04 ±5.3

113.5 7.59E-05 3.47E-05 9.46E-06 1.58E-05 7.79E-03 3.48E-03 8.23E-04 8.54E-04 ±5.2

114.0 8.10E-05 3.71E-05 1.01E-05 1.69E-05 8.25E-03 3.69E-03 8.73E-04 9.04E-04 ±5.2

114.5 8.64E-05 3.95E-05 1.07E-05 1.81E-05 8.73E-03 3.91E-03 9.25E-04 9.56E-04 ±5.2

115.0 9.22E-05 4.21E-05 1.14E-05 1.93E-05 9.23E-03 4.13E-03 9.79E-04 1.01E-03 ±5.2

115.5 9.82E-05 4.48E-05 1.21E-05 2.06E-05 9.74E-03 4.36E-03 1.03E-03 1.06E-03 ±5.1

116.0 1.05E-04 4.77E-05 1.28E-05 2.20E-05 1.03E-02 4.61E-03 1.09E-03 1.12E-03 ±5.1

116.5 1.11E-04 5.07E-05 1.36E-05 2.35E-05 1.08E-02 4.86E-03 1.15E-03 1.18E-03 ±5.0

117.0 1.18E-04 5.38E-05 1.44E-05 2.50E-05 1.14E-02 5.12E-03 1.22E-03 1.24E-03 ±5.0

117.5 1.26E-04 5.71E-05 1.53E-05 2.65E-05 1.20E-02 5.39E-03 1.28E-03 1.31E-03 ±5.0

118.0 1.33E-04 6.06E-05 1.62E-05 2.82E-05 1.26E-02 5.67E-03 1.35E-03 1.38E-03 ±4.9

118.5 1.41E-04 6.42E-05 1.71E-05 2.99E-05 1.33E-02 5.96E-03 1.42E-03 1.44E-03 ±4.9

119.0 1.50E-04 6.79E-05 1.81E-05 3.18E-05 1.39E-02 6.26E-03 1.49E-03 1.51E-03 ±4.8

119.5 1.58E-04 7.18E-05 1.91E-05 3.37E-05 1.46E-02 6.57E-03 1.56E-03 1.59E-03 ±4.8

120.0 1.67E-04 7.59E-05 2.01E-05 3.56E-05 1.53E-02 6.89E-03 1.64E-03 1.66E-03 ±4.8

120.5 1.77E-04 8.01E-05 2.12E-05 3.76E-05 1.60E-02 7.21E-03 1.72E-03 1.74E-03 ±4.7

121.0 1.86E-04 8.45E-05 2.24E-05 3.98E-05 1.68E-02 7.55E-03 1.80E-03 1.82E-03 ±4.7

121.5 1.96E-04 8.90E-05 2.35E-05 4.19E-05 1.75E-02 7.90E-03 1.88E-03 1.90E-03 ±4.6

122.0 2.07E-04 9.36E-05 2.47E-05 4.42E-05 1.83E-02 8.25E-03 1.97E-03 1.98E-03 ±4.6

122.5 2.18E-04 9.85E-05 2.60E-05 4.65E-05 1.91E-02 8.61E-03 2.05E-03 2.07E-03 ±4.5

123.0 2.29E-04 1.03E-04 2.72E-05 4.90E-05 1.99E-02 8.99E-03 2.14E-03 2.16E-03 ±4.5

123.5 2.40E-04 1.09E-04 2.86E-05 5.14E-05 2.08E-02 9.37E-03 2.23E-03 2.24E-03 ±4.4

124.0 2.52E-04 1.14E-04 2.99E-05 5.40E-05 2.16E-02 9.76E-03 2.33E-03 2.34E-03 ±4.4

124.5 2.64E-04 1.19E-04 3.13E-05 5.66E-05 2.25E-02 1.02E-02 2.42E-03 2.43E-03 ±4.3

125.0 2.76E-04 1.25E-04 3.27E-05 5.93E-05 2.34E-02 1.06E-02 2.52E-03 2.52E-03 ±4.3

125.5 2.89E-04 1.30E-04 3.42E-05 6.21E-05 2.43E-02 1.10E-02 2.62E-03 2.62E-03 ±4.2

126.0 3.02E-04 1.36E-04 3.56E-05 6.49E-05 2.53E-02 1.14E-02 2.72E-03 2.72E-03 ±4.1

126.5 3.15E-04 1.42E-04 3.72E-05 6.78E-05 2.62E-02 1.18E-02 2.83E-03 2.82E-03 ±4.1

127.0 3.28E-04 1.48E-04 3.87E-05 7.08E-05 2.72E-02 1.23E-02 2.93E-03 2.92E-03 ±4.0

127.5 3.42E-04 1.54E-04 4.03E-05 7.38E-05 2.81E-02 1.27E-02 3.04E-03 3.02E-03 ±4.0

128.0 3.56E-04 1.61E-04 4.19E-05 7.68E-05 2.91E-02 1.32E-02 3.15E-03 3.13E-03 ±3.9

128.5 3.70E-04 1.67E-04 4.35E-05 8.00E-05 3.01E-02 1.36E-02 3.26E-03 3.24E-03 ±3.8

129.0 3.85E-04 1.73E-04 4.52E-05 8.31E-05 3.12E-02 1.41E-02 3.37E-03 3.34E-03 ±3.8

129.5 3.99E-04 1.80E-04 4.68E-05 8.63E-05 3.22E-02 1.46E-02 3.48E-03 3.45E-03 ±3.7

130.0 4.14E-04 1.87E-04 4.85E-05 8.96E-05 3.32E-02 1.50E-02 3.60E-03 3.56E-03 ±3.7

November 18, 2011 – 11 : 26 DRAFT 24

Table 16: SM Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their total uncertain-ties (expressed in percentage). Low and intermediate mass range.



ν = any ν = any

130.5 4.29E-04 1.93E-04 5.02E-05 9.29E-05 3.43E-02 1.55E-02 3.71E-03 3.67E-03 ±3.6

131.0 4.44E-04 2.00E-04 5.19E-05 9.62E-05 3.54E-02 1.60E-02 3.83E-03 3.79E-03 ±3.5

131.5 4.59E-04 2.07E-04 5.37E-05 9.95E-05 3.64E-02 1.65E-02 3.94E-03 3.90E-03 ±3.5

132.0 4.75E-04 2.14E-04 5.54E-05 1.03E-04 3.75E-02 1.70E-02 4.06E-03 4.01E-03 ±3.4

132.5 4.90E-04 2.21E-04 5.71E-05 1.06E-04 3.86E-02 1.75E-02 4.18E-03 4.13E-03 ±3.3

133.0 5.05E-04 2.27E-04 5.89E-05 1.10E-04 3.97E-02 1.80E-02 4.30E-03 4.24E-03 ±3.3

133.5 5.21E-04 2.34E-04 6.06E-05 1.13E-04 4.08E-02 1.85E-02 4.43E-03 4.36E-03 ±3.2

134.0 5.36E-04 2.41E-04 6.24E-05 1.16E-04 4.19E-02 1.90E-02 4.55E-03 4.48E-03 ±3.1

134.5 5.52E-04 2.48E-04 6.41E-05 1.20E-04 4.30E-02 1.95E-02 4.67E-03 4.59E-03 ±3.1

135.0 5.67E-04 2.55E-04 6.58E-05 1.23E-04 4.41E-02 2.00E-02 4.79E-03 4.71E-03 ±3.0

135.5 5.82E-04 2.62E-04 6.76E-05 1.26E-04 4.52E-02 2.05E-02 4.92E-03 4.83E-03 ±2.9

136.0 5.97E-04 2.68E-04 6.93E-05 1.30E-04 4.64E-02 2.10E-02 5.04E-03 4.95E-03 ±2.8

136.5 6.12E-04 2.75E-04 7.10E-05 1.33E-04 4.75E-02 2.15E-02 5.16E-03 5.07E-03 ±2.6

137.0 6.27E-04 2.82E-04 7.26E-05 1.36E-04 4.86E-02 2.20E-02 5.29E-03 5.19E-03 ±2.5

137.5 6.42E-04 2.88E-04 7.43E-05 1.40E-04 4.97E-02 2.25E-02 5.41E-03 5.31E-03 ±2.4

138.0 6.56E-04 2.94E-04 7.59E-05 1.43E-04 5.09E-02 2.31E-02 5.54E-03 5.42E-03 ±2.2

138.5 6.70E-04 3.01E-04 7.75E-05 1.46E-04 5.20E-02 2.36E-02 5.66E-03 5.54E-03 ±2.1

139.0 6.84E-04 3.07E-04 7.90E-05 1.49E-04 5.31E-02 2.41E-02 5.78E-03 5.66E-03 ±1.9

139.5 6.97E-04 3.13E-04 8.05E-05 1.52E-04 5.42E-02 2.46E-02 5.91E-03 5.78E-03 ±1.8

140.0 7.11E-04 3.19E-04 8.20E-05 1.55E-04 5.53E-02 2.51E-02 6.03E-03 5.90E-03 ±1.7

141.0 7.36E-04 3.30E-04 8.48E-05 1.60E-04 5.76E-02 2.61E-02 6.28E-03 6.14E-03 ±1.6

142.0 7.59E-04 3.41E-04 8.75E-05 1.66E-04 5.98E-02 2.71E-02 6.52E-03 6.37E-03 ±1.5

143.0 7.81E-04 3.50E-04 8.99E-05 1.70E-04 6.20E-02 2.81E-02 6.76E-03 6.61E-03 ±1.4

144.0 8.00E-04 3.59E-04 9.20E-05 1.75E-04 6.41E-02 2.91E-02 7.00E-03 6.84E-03 ±1.3

145.0 8.17E-04 3.66E-04 9.38E-05 1.78E-04 6.63E-02 3.00E-02 7.24E-03 7.07E-03 ±1.2

146.0 8.31E-04 3.72E-04 9.53E-05 1.82E-04 6.84E-02 3.10E-02 7.48E-03 7.30E-03 ±1.2

147.0 8.41E-04 3.77E-04 9.65E-05 1.84E-04 7.05E-02 3.20E-02 7.72E-03 7.53E-03 ±1.1

148.0 8.48E-04 3.80E-04 9.72E-05 1.86E-04 7.26E-02 3.29E-02 7.95E-03 7.75E-03 ±1.0

149.0 8.51E-04 3.81E-04 9.75E-05 1.86E-04 7.46E-02 3.38E-02 8.18E-03 7.98E-03 ±0.9

150.0 8.50E-04 3.81E-04 9.72E-05 1.86E-04 7.67E-02 3.47E-02 8.41E-03 8.20E-03 ±0.9

151.0 8.43E-04 3.78E-04 9.64E-05 1.85E-04 7.87E-02 3.56E-02 8.64E-03 8.43E-03 ±0.8

152.0 8.31E-04 3.72E-04 9.50E-05 1.82E-04 8.07E-02 3.65E-02 8.86E-03 8.66E-03 ±0.7

153.0 8.13E-04 3.64E-04 9.29E-05 1.78E-04 8.27E-02 3.74E-02 9.10E-03 8.89E-03 ±0.7

154.0 7.88E-04 3.53E-04 8.99E-05 1.73E-04 8.48E-02 3.83E-02 9.33E-03 9.12E-03 ±0.6

155.0 7.55E-04 3.38E-04 8.60E-05 1.65E-04 8.69E-02 3.92E-02 9.57E-03 9.36E-03 ±0.5

156.0 7.11E-04 3.18E-04 8.11E-05 1.56E-04 8.90E-02 4.01E-02 9.81E-03 9.61E-03 ±0.5

157.0 6.57E-04 2.94E-04 7.49E-05 1.44E-04 9.11E-02 4.10E-02 1.01E-02 9.87E-03 ±0.4

158.0 5.91E-04 2.64E-04 6.73E-05 1.30E-04 9.33E-02 4.19E-02 1.03E-02 1.01E-02 ±0.3

159.0 5.12E-04 2.29E-04 5.82E-05 1.12E-04 9.56E-02 4.29E-02 1.06E-02 1.04E-02 ±0.3

160.0 4.25E-04 1.90E-04 4.83E-05 9.34E-05 9.79E-02 4.38E-02 1.08E-02 1.07E-02 ±0.2

162.0 2.89E-04 1.29E-04 3.28E-05 6.35E-05 1.01E-01 4.52E-02 1.12E-02 1.11E-02 ±0.2

164.0 2.37E-04 1.06E-04 2.69E-05 5.21E-05 1.02E-01 4.57E-02 1.14E-02 1.13E-02 ±0.1

166.0 2.23E-04 9.98E-05 2.53E-05 4.92E-05 1.03E-01 4.59E-02 1.14E-02 1.13E-02 ±0.1

168.0 2.27E-04 1.01E-04 2.57E-05 5.00E-05 1.03E-01 4.60E-02 1.15E-02 1.14E-02 ±0.1

170.0 2.41E-04 1.08E-04 2.73E-05 5.32E-05 1.03E-01 4.61E-02 1.15E-02 1.14E-02 ±0.1

November 18, 2011 – 11 : 26 DRAFT 25

Table 17: SM Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their total uncertain-ties (expressed in percentage). Intermediate mass range.



ν = any ν = any

172.0 2.66E-04 1.19E-04 3.00E-05 5.87E-05 1.03E-01 4.61E-02 1.15E-02 1.14E-02 ±0.0

174.0 3.04E-04 1.36E-04 3.42E-05 6.71E-05 1.03E-01 4.61E-02 1.14E-02 1.13E-02 ±0.0

176.0 3.61E-04 1.61E-04 4.06E-05 7.98E-05 1.03E-01 4.60E-02 1.14E-02 1.13E-02 ±0.0

178.0 4.52E-04 2.01E-04 5.07E-05 9.99E-05 1.02E-01 4.58E-02 1.13E-02 1.12E-02 ±0.0

180.0 6.12E-04 2.73E-04 6.85E-05 1.36E-04 1.01E-01 4.55E-02 1.12E-02 1.10E-02 ±0.0

182.0 9.14E-04 4.07E-04 1.02E-04 2.03E-04 9.94E-02 4.50E-02 1.10E-02 1.06E-02 ±0.0

184.0 1.33E-03 5.93E-04 1.49E-04 2.96E-04 9.67E-02 4.42E-02 1.07E-02 1.02E-02 ±0.0

186.0 1.69E-03 7.50E-04 1.88E-04 3.75E-04 9.45E-02 4.35E-02 1.05E-02 9.76E-03 ±0.0

188.0 1.94E-03 8.62E-04 2.16E-04 4.31E-04 9.29E-02 4.30E-02 1.03E-02 9.47E-03 ±0.0

190.0 2.12E-03 9.44E-04 2.36E-04 4.72E-04 9.18E-02 4.27E-02 1.02E-02 9.26E-03 ±0.0

192.0 2.26E-03 1.01E-03 2.52E-04 5.03E-04 9.09E-02 4.24E-02 1.01E-02 9.10E-03 ±0.0

194.0 2.37E-03 1.05E-03 2.64E-04 5.27E-04 9.02E-02 4.22E-02 1.00E-02 8.98E-03 ±0.0

196.0 2.46E-03 1.09E-03 2.74E-04 5.46E-04 8.97E-02 4.20E-02 9.96E-03 8.88E-03 ±0.0

198.0 2.53E-03 1.12E-03 2.81E-04 5.62E-04 8.92E-02 4.19E-02 9.91E-03 8.80E-03 ±0.0

200.0 2.59E-03 1.15E-03 2.88E-04 5.75E-04 8.89E-02 4.18E-02 9.87E-03 8.73E-03 ±0.0

202.0 2.64E-03 1.17E-03 2.93E-04 5.86E-04 8.86E-02 4.17E-02 9.84E-03 8.67E-03 ±0.0

204.0 2.68E-03 1.19E-03 2.98E-04 5.96E-04 8.83E-02 4.16E-02 9.81E-03 8.62E-03 ±0.0

206.0 2.72E-03 1.21E-03 3.02E-04 6.04E-04 8.81E-02 4.16E-02 9.78E-03 8.58E-03 ±0.0

208.0 2.75E-03 1.22E-03 3.05E-04 6.11E-04 8.79E-02 4.15E-02 9.76E-03 8.55E-03 ±0.0

210.0 2.78E-03 1.23E-03 3.08E-04 6.17E-04 8.77E-02 4.14E-02 9.74E-03 8.52E-03 ±0.0

212.0 2.80E-03 1.24E-03 3.11E-04 6.22E-04 8.76E-02 4.14E-02 9.73E-03 8.49E-03 ±0.0

214.0 2.82E-03 1.25E-03 3.13E-04 6.27E-04 8.74E-02 4.14E-02 9.71E-03 8.47E-03 ±0.0

216.0 2.84E-03 1.26E-03 3.16E-04 6.31E-04 8.73E-02 4.13E-02 9.70E-03 8.45E-03 ±0.0

218.0 2.86E-03 1.27E-03 3.17E-04 6.35E-04 8.72E-02 4.13E-02 9.69E-03 8.43E-03 ±0.0

220.0 2.87E-03 1.28E-03 3.19E-04 6.38E-04 8.71E-02 4.13E-02 9.68E-03 8.41E-03 ±0.0

222.0 2.89E-03 1.28E-03 3.21E-04 6.41E-04 8.70E-02 4.12E-02 9.67E-03 8.39E-03 ±0.0

224.0 2.90E-03 1.29E-03 3.22E-04 6.44E-04 8.70E-02 4.12E-02 9.66E-03 8.38E-03 ±0.0

226.0 2.91E-03 1.29E-03 3.24E-04 6.47E-04 8.69E-02 4.12E-02 9.65E-03 8.36E-03 ±0.0

228.0 2.92E-03 1.30E-03 3.25E-04 6.49E-04 8.68E-02 4.12E-02 9.65E-03 8.35E-03 ±0.0

230.0 2.93E-03 1.30E-03 3.26E-04 6.52E-04 8.68E-02 4.12E-02 9.64E-03 8.34E-03 ±0.0

232.0 2.94E-03 1.31E-03 3.27E-04 6.54E-04 8.67E-02 4.11E-02 9.63E-03 8.33E-03 ±0.0

234.0 2.95E-03 1.31E-03 3.28E-04 6.56E-04 8.67E-02 4.11E-02 9.63E-03 8.32E-03 ±0.0

236.0 2.96E-03 1.32E-03 3.29E-04 6.58E-04 8.66E-02 4.11E-02 9.62E-03 8.31E-03 ±0.0

238.0 2.97E-03 1.32E-03 3.30E-04 6.59E-04 8.66E-02 4.11E-02 9.62E-03 8.30E-03 ±0.0

240.0 2.97E-03 1.32E-03 3.31E-04 6.61E-04 8.65E-02 4.11E-02 9.61E-03 8.29E-03 ±0.0

242.0 2.98E-03 1.32E-03 3.31E-04 6.62E-04 8.65E-02 4.11E-02 9.61E-03 8.29E-03 ±0.0

244.0 2.99E-03 1.33E-03 3.32E-04 6.64E-04 8.64E-02 4.11E-02 9.60E-03 8.28E-03 ±0.0

246.0 2.99E-03 1.33E-03 3.33E-04 6.65E-04 8.64E-02 4.10E-02 9.60E-03 8.27E-03 ±0.0

248.0 3.00E-03 1.33E-03 3.33E-04 6.67E-04 8.64E-02 4.10E-02 9.59E-03 8.27E-03 ±0.0

250.0 3.01E-03 1.34E-03 3.34E-04 6.68E-04 8.63E-02 4.10E-02 9.59E-03 8.26E-03 ±0.0

252.0 3.01E-03 1.34E-03 3.35E-04 6.69E-04 8.63E-02 4.10E-02 9.59E-03 8.25E-03 ±0.0

254.0 3.02E-03 1.34E-03 3.35E-04 6.70E-04 8.62E-02 4.10E-02 9.58E-03 8.25E-03 ±0.0

256.0 3.02E-03 1.34E-03 3.36E-04 6.71E-04 8.62E-02 4.10E-02 9.58E-03 8.24E-03 ±0.0

258.0 3.03E-03 1.35E-03 3.37E-04 6.73E-04 8.62E-02 4.10E-02 9.58E-03 8.24E-03 ±0.0

260.0 3.03E-03 1.35E-03 3.37E-04 6.74E-04 8.62E-02 4.10E-02 9.57E-03 8.23E-03 ±0.0

November 18, 2011 – 11 : 26 DRAFT 26

Table 18: SM Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their total uncertain-ties (expressed in percentage). High mass range.



ν = any ν = any

262.0 3.04E-03 1.35E-03 3.38E-04 6.75E-04 8.61E-02 4.10E-02 9.57E-03 8.22E-03 ±0.0

264.0 3.04E-03 1.35E-03 3.38E-04 6.76E-04 8.61E-02 4.10E-02 9.57E-03 8.22E-03 ±0.0

266.0 3.05E-03 1.35E-03 3.39E-04 6.77E-04 8.61E-02 4.09E-02 9.56E-03 8.21E-03 ±0.0

268.0 3.05E-03 1.36E-03 3.39E-04 6.78E-04 8.60E-02 4.09E-02 9.56E-03 8.21E-03 ±0.0

270.0 3.05E-03 1.36E-03 3.40E-04 6.79E-04 8.60E-02 4.09E-02 9.56E-03 8.21E-03 ±0.0

272.0 3.06E-03 1.36E-03 3.40E-04 6.80E-04 8.60E-02 4.09E-02 9.55E-03 8.20E-03 ±0.0

274.0 3.06E-03 1.36E-03 3.40E-04 6.80E-04 8.60E-02 4.09E-02 9.55E-03 8.20E-03 ±0.0

276.0 3.07E-03 1.36E-03 3.41E-04 6.81E-04 8.59E-02 4.09E-02 9.55E-03 8.19E-03 ±0.0

278.0 3.07E-03 1.36E-03 3.41E-04 6.82E-04 8.59E-02 4.09E-02 9.55E-03 8.19E-03 ±0.0

280.0 3.07E-03 1.37E-03 3.42E-04 6.83E-04 8.59E-02 4.09E-02 9.54E-03 8.18E-03 ±0.0

282.0 3.08E-03 1.37E-03 3.42E-04 6.84E-04 8.59E-02 4.09E-02 9.54E-03 8.18E-03 ±0.0

284.0 3.08E-03 1.37E-03 3.43E-04 6.85E-04 8.59E-02 4.09E-02 9.54E-03 8.18E-03 ±0.0

286.0 3.08E-03 1.37E-03 3.43E-04 6.85E-04 8.58E-02 4.09E-02 9.54E-03 8.17E-03 ±0.0

288.0 3.09E-03 1.37E-03 3.43E-04 6.86E-04 8.58E-02 4.09E-02 9.53E-03 8.17E-03 ±0.0

290.0 3.09E-03 1.37E-03 3.44E-04 6.87E-04 8.58E-02 4.09E-02 9.53E-03 8.16E-03 ±0.0

295.0 3.10E-03 1.38E-03 3.45E-04 6.88E-04 8.57E-02 4.08E-02 9.53E-03 8.15E-03 ±0.0

300.0 3.11E-03 1.38E-03 3.45E-04 6.90E-04 8.57E-02 4.08E-02 9.52E-03 8.15E-03 ±0.0

305.0 3.11E-03 1.38E-03 3.46E-04 6.92E-04 8.56E-02 4.08E-02 9.52E-03 8.14E-03 ±0.0

310.0 3.12E-03 1.39E-03 3.47E-04 6.93E-04 8.56E-02 4.08E-02 9.51E-03 8.13E-03 ±0.0

315.0 3.13E-03 1.39E-03 3.48E-04 6.94E-04 8.56E-02 4.08E-02 9.51E-03 8.12E-03 ±0.0

320.0 3.13E-03 1.39E-03 3.48E-04 6.96E-04 8.55E-02 4.08E-02 9.50E-03 8.11E-03 ±0.0

325.0 3.14E-03 1.39E-03 3.49E-04 6.97E-04 8.55E-02 4.08E-02 9.49E-03 8.11E-03 ±0.0

330.0 3.14E-03 1.40E-03 3.49E-04 6.98E-04 8.54E-02 4.07E-02 9.49E-03 8.10E-03 ±0.0

335.0 3.14E-03 1.40E-03 3.50E-04 6.99E-04 8.54E-02 4.07E-02 9.48E-03 8.09E-03 ±0.0

340.0 3.15E-03 1.40E-03 3.50E-04 6.99E-04 8.53E-02 4.07E-02 9.48E-03 8.08E-03 ±0.0

345.0 3.14E-03 1.40E-03 3.49E-04 6.98E-04 8.51E-02 4.06E-02 9.45E-03 8.06E-03 ±0.7

350.0 3.11E-03 1.38E-03 3.45E-04 6.90E-04 8.40E-02 4.01E-02 9.33E-03 7.96E-03 ±1.4

360.0 3.00E-03 1.33E-03 3.34E-04 6.67E-04 8.09E-02 3.86E-02 8.99E-03 7.66E-03 ±2.6

370.0 2.91E-03 1.29E-03 3.23E-04 6.46E-04 7.82E-02 3.73E-02 8.68E-03 7.40E-03 ±2.9

380.0 2.83E-03 1.26E-03 3.15E-04 6.29E-04 7.59E-02 3.62E-02 8.43E-03 7.18E-03 ±3.1

390.0 2.77E-03 1.23E-03 3.08E-04 6.16E-04 7.40E-02 3.54E-02 8.23E-03 7.00E-03 ±3.1

400.0 2.73E-03 1.21E-03 3.03E-04 6.06E-04 7.26E-02 3.47E-02 8.06E-03 6.86E-03 ±3.1

410.0 2.69E-03 1.20E-03 2.99E-04 5.98E-04 7.14E-02 3.41E-02 7.94E-03 6.75E-03 ±3.1

420.0 2.67E-03 1.19E-03 2.96E-04 5.93E-04 7.06E-02 3.37E-02 7.84E-03 6.66E-03 ±3.1

430.0 2.65E-03 1.18E-03 2.94E-04 5.89E-04 6.99E-02 3.34E-02 7.76E-03 6.59E-03 ±3.0

440.0 2.64E-03 1.17E-03 2.93E-04 5.86E-04 6.94E-02 3.32E-02 7.71E-03 6.54E-03 ±3.0

450.0 2.63E-03 1.17E-03 2.92E-04 5.85E-04 6.90E-02 3.30E-02 7.67E-03 6.50E-03 ±2.9

460.0 2.63E-03 1.17E-03 2.92E-04 5.84E-04 6.88E-02 3.29E-02 7.64E-03 6.48E-03 ±2.8

470.0 2.63E-03 1.17E-03 2.92E-04 5.84E-04 6.86E-02 3.28E-02 7.62E-03 6.46E-03 ±2.8

480.0 2.63E-03 1.17E-03 2.93E-04 5.85E-04 6.85E-02 3.28E-02 7.61E-03 6.45E-03 ±2.7

490.0 2.64E-03 1.17E-03 2.93E-04 5.87E-04 6.85E-02 3.28E-02 7.61E-03 6.44E-03 ±2.6

500.0 2.65E-03 1.18E-03 2.94E-04 5.88E-04 6.85E-02 3.28E-02 7.61E-03 6.44E-03 ±2.4

510.0 2.66E-03 1.18E-03 2.95E-04 5.90E-04 6.86E-02 3.28E-02 7.62E-03 6.45E-03 ±2.3

520.0 2.67E-03 1.18E-03 2.96E-04 5.92E-04 6.87E-02 3.29E-02 7.64E-03 6.46E-03 ±2.4

530.0 2.68E-03 1.19E-03 2.97E-04 5.95E-04 6.89E-02 3.30E-02 7.65E-03 6.47E-03 ±2.4

540.0 2.69E-03 1.19E-03 2.99E-04 5.97E-04 6.90E-02 3.31E-02 7.67E-03 6.48E-03 ±2.4

November 18, 2011 – 11 : 26 DRAFT 27

Table 19: SM Higgs branching ratios for the differentH → 4l andH → 2l2ν final states and their total uncertain-ties (expressed in percentage). Very high mass range.



ν = any ν = any

550.0 2.70E-03 1.20E-03 3.00E-04 6.00E-04 6.92E-02 3.32E-02 7.69E-03 6.50E-03 ±2.4

560.0 2.71E-03 1.21E-03 3.01E-04 6.03E-04 6.94E-02 3.33E-02 7.71E-03 6.51E-03 ±2.5

570.0 2.73E-03 1.21E-03 3.03E-04 6.06E-04 6.96E-02 3.34E-02 7.74E-03 6.53E-03 ±2.5

580.0 2.74E-03 1.22E-03 3.04E-04 6.09E-04 6.99E-02 3.35E-02 7.76E-03 6.55E-03 ±2.5

590.0 2.75E-03 1.22E-03 3.06E-04 6.12E-04 7.01E-02 3.36E-02 7.79E-03 6.57E-03 ±2.5

600.0 2.77E-03 1.23E-03 3.07E-04 6.15E-04 7.03E-02 3.37E-02 7.82E-03 6.59E-03 ±2.5

610.0 2.78E-03 1.24E-03 3.09E-04 6.18E-04 7.06E-02 3.38E-02 7.84E-03 6.61E-03 ±2.5

620.0 2.79E-03 1.24E-03 3.10E-04 6.21E-04 7.08E-02 3.40E-02 7.87E-03 6.64E-03 ±2.6

630.0 2.81E-03 1.25E-03 3.12E-04 6.24E-04 7.11E-02 3.41E-02 7.90E-03 6.66E-03 ±2.5

640.0 2.82E-03 1.25E-03 3.13E-04 6.27E-04 7.14E-02 3.42E-02 7.93E-03 6.68E-03 ±2.6

650.0 2.83E-03 1.26E-03 3.15E-04 6.29E-04 7.16E-02 3.43E-02 7.96E-03 6.71E-03 ±2.6

660.0 2.85E-03 1.26E-03 3.16E-04 6.32E-04 7.19E-02 3.45E-02 7.99E-03 6.73E-03 ±2.6

670.0 2.86E-03 1.27E-03 3.18E-04 6.35E-04 7.21E-02 3.46E-02 8.02E-03 6.75E-03 ±2.6

680.0 2.87E-03 1.28E-03 3.19E-04 6.38E-04 7.24E-02 3.47E-02 8.04E-03 6.77E-03 ±2.6

690.0 2.88E-03 1.28E-03 3.20E-04 6.41E-04 7.26E-02 3.48E-02 8.07E-03 6.80E-03 ±2.6

700.0 2.90E-03 1.29E-03 3.22E-04 6.44E-04 7.29E-02 3.50E-02 8.10E-03 6.82E-03 ±2.6

710.0 2.91E-03 1.29E-03 3.23E-04 6.46E-04 7.31E-02 3.51E-02 8.13E-03 6.84E-03 ±2.6

720.0 2.92E-03 1.30E-03 3.24E-04 6.49E-04 7.34E-02 3.52E-02 8.16E-03 6.86E-03 ±2.6

730.0 2.93E-03 1.30E-03 3.26E-04 6.52E-04 7.37E-02 3.53E-02 8.18E-03 6.89E-03 ±2.6

740.0 2.94E-03 1.31E-03 3.27E-04 6.54E-04 7.39E-02 3.54E-02 8.21E-03 6.91E-03 ±2.6

750.0 2.95E-03 1.31E-03 3.28E-04 6.57E-04 7.41E-02 3.56E-02 8.24E-03 6.93E-03 ±2.6

760.0 2.97E-03 1.32E-03 3.30E-04 6.59E-04 7.44E-02 3.57E-02 8.26E-03 6.95E-03 ±2.6

770.0 2.98E-03 1.32E-03 3.31E-04 6.62E-04 7.46E-02 3.58E-02 8.29E-03 6.97E-03 ±2.6

780.0 2.99E-03 1.33E-03 3.32E-04 6.64E-04 7.48E-02 3.59E-02 8.32E-03 6.99E-03 ±2.6

790.0 3.00E-03 1.33E-03 3.33E-04 6.67E-04 7.51E-02 3.60E-02 8.34E-03 7.02E-03 ±2.7

800.0 3.01E-03 1.34E-03 3.34E-04 6.69E-04 7.53E-02 3.61E-02 8.37E-03 7.04E-03 ±2.7

810.0 3.02E-03 1.34E-03 3.35E-04 6.71E-04 7.55E-02 3.62E-02 8.39E-03 7.06E-03 ±2.7

820.0 3.03E-03 1.35E-03 3.37E-04 6.73E-04 7.57E-02 3.63E-02 8.42E-03 7.08E-03 ±2.7

830.0 3.04E-03 1.35E-03 3.38E-04 6.75E-04 7.60E-02 3.64E-02 8.44E-03 7.10E-03 ±2.7

840.0 3.05E-03 1.36E-03 3.39E-04 6.78E-04 7.62E-02 3.65E-02 8.46E-03 7.12E-03 ±2.7

850.0 3.06E-03 1.36E-03 3.40E-04 6.80E-04 7.64E-02 3.67E-02 8.49E-03 7.13E-03 ±2.7

860.0 3.07E-03 1.36E-03 3.41E-04 6.82E-04 7.66E-02 3.67E-02 8.51E-03 7.15E-03 ±2.7

870.0 3.08E-03 1.37E-03 3.42E-04 6.84E-04 7.68E-02 3.68E-02 8.53E-03 7.17E-03 ±2.7

880.0 3.09E-03 1.37E-03 3.43E-04 6.86E-04 7.70E-02 3.69E-02 8.55E-03 7.19E-03 ±2.8

890.0 3.09E-03 1.38E-03 3.44E-04 6.88E-04 7.72E-02 3.70E-02 8.58E-03 7.21E-03 ±2.8

900.0 3.10E-03 1.38E-03 3.45E-04 6.89E-04 7.74E-02 3.71E-02 8.60E-03 7.23E-03 ±2.8

910.0 3.11E-03 1.38E-03 3.46E-04 6.91E-04 7.76E-02 3.72E-02 8.62E-03 7.24E-03 ±2.8

920.0 3.12E-03 1.39E-03 3.47E-04 6.93E-04 7.78E-02 3.73E-02 8.64E-03 7.26E-03 ±2.8

930.0 3.13E-03 1.39E-03 3.48E-04 6.95E-04 7.79E-02 3.74E-02 8.66E-03 7.28E-03 ±2.8

940.0 3.14E-03 1.39E-03 3.48E-04 6.97E-04 7.81E-02 3.75E-02 8.68E-03 7.29E-03 ±2.8

950.0 3.14E-03 1.40E-03 3.49E-04 6.98E-04 7.83E-02 3.76E-02 8.70E-03 7.31E-03 ±2.8

960.0 3.15E-03 1.40E-03 3.50E-04 7.00E-04 7.85E-02 3.77E-02 8.72E-03 7.33E-03 ±2.8

970.0 3.16E-03 1.40E-03 3.51E-04 7.02E-04 7.86E-02 3.77E-02 8.74E-03 7.34E-03 ±2.8

980.0 3.17E-03 1.41E-03 3.52E-04 7.04E-04 7.88E-02 3.78E-02 8.76E-03 7.36E-03 ±2.9

990.0 3.17E-03 1.41E-03 3.53E-04 7.05E-04 7.90E-02 3.79E-02 8.78E-03 7.37E-03 ±2.9

1000.0 3.18E-03 1.41E-03 3.53E-04 7.07E-04 7.91E-02 3.80E-02 8.80E-03 7.39E-03 ±2.9

November 18, 2011 – 11 : 26 DRAFT 28

Table 20: SM Higgs branching ratios for the different four-fermion final states and their total uncertainties (ex-pressed in percentage). Very low mass range.

MH H → 2l2q H → 2l2q H → lνlqq H → ννqq H → 4q H → 4f ∆BR

[ GeV] l = e, µ, τ l = e, µ l = e, µ ν = any q = udcsb f = any [%]

q = udcsb q = udcsb q = udcsb q = udcsb fermion

90.0 5.87E-05 3.91E-05 3.03E-04 1.18E-04 1.05E-03 2.37E-03 ±5.8

95.0 9.31E-05 6.21E-05 6.85E-04 1.87E-04 2.32E-03 5.17E-03 ±5.8

100.0 1.57E-04 1.04E-04 1.61E-03 3.14E-04 5.34E-03 1.18E-02 ±5.7

105.0 2.97E-04 1.98E-04 3.52E-03 5.95E-04 1.17E-02 2.58E-02 ±5.6

110.0 6.06E-04 4.04E-04 6.99E-03 1.21E-03 2.34E-02 5.15E-02 ±5.4

110.5 6.50E-04 4.34E-04 7.44E-03 1.30E-03 2.50E-02 5.49E-02 ±5.4

111.0 6.98E-04 4.66E-04 7.92E-03 1.40E-03 2.66E-02 5.85E-02 ±5.4

111.5 7.50E-04 5.00E-04 8.42E-03 1.50E-03 2.83E-02 6.23E-02 ±5.4

112.0 8.04E-04 5.36E-04 8.94E-03 1.61E-03 3.01E-02 6.62E-02 ±5.3

112.5 8.62E-04 5.75E-04 9.48E-03 1.72E-03 3.20E-02 7.03E-02 ±5.3

113.0 9.23E-04 6.16E-04 1.01E-02 1.85E-03 3.40E-02 7.46E-02 ±5.3

113.5 9.89E-04 6.59E-04 1.06E-02 1.98E-03 3.60E-02 7.91E-02 ±5.2

114.0 1.06E-03 7.05E-04 1.13E-02 2.11E-03 3.81E-02 8.38E-02 ±5.2

114.5 1.13E-03 7.54E-04 1.19E-02 2.26E-03 4.04E-02 8.87E-02 ±5.2

115.0 1.21E-03 8.05E-04 1.26E-02 2.41E-03 4.27E-02 9.38E-02 ±5.2

115.5 1.29E-03 8.59E-04 1.33E-02 2.58E-03 4.51E-02 9.90E-02 ±5.1

116.0 1.37E-03 9.16E-04 1.40E-02 2.75E-03 4.76E-02 1.05E-01 ±5.1

116.5 1.46E-03 9.76E-04 1.47E-02 2.93E-03 5.03E-02 1.10E-01 ±5.0

117.0 1.56E-03 1.04E-03 1.55E-02 3.11E-03 5.30E-02 1.16E-01 ±5.0

117.5 1.66E-03 1.10E-03 1.63E-02 3.31E-03 5.58E-02 1.22E-01 ±5.0

118.0 1.76E-03 1.17E-03 1.71E-02 3.52E-03 5.87E-02 1.29E-01 ±4.9

118.5 1.87E-03 1.25E-03 1.80E-02 3.73E-03 6.17E-02 1.35E-01 ±4.9

119.0 1.98E-03 1.32E-03 1.89E-02 3.96E-03 6.48E-02 1.42E-01 ±4.8

119.5 2.10E-03 1.40E-03 1.98E-02 4.19E-03 6.80E-02 1.49E-01 ±4.8

120.0 2.22E-03 1.48E-03 2.07E-02 4.44E-03 7.13E-02 1.56E-01 ±4.8

120.5 2.35E-03 1.57E-03 2.16E-02 4.69E-03 7.47E-02 1.64E-01 ±4.7

121.0 2.48E-03 1.65E-03 2.26E-02 4.95E-03 7.82E-02 1.71E-01 ±4.7

121.5 2.62E-03 1.74E-03 2.36E-02 5.22E-03 8.18E-02 1.79E-01 ±4.6

122.0 2.76E-03 1.84E-03 2.47E-02 5.50E-03 8.55E-02 1.87E-01 ±4.6

122.5 2.90E-03 1.94E-03 2.57E-02 5.80E-03 8.92E-02 1.95E-01 ±4.5

123.0 3.06E-03 2.04E-03 2.68E-02 6.10E-03 9.31E-02 2.04E-01 ±4.5

123.5 3.21E-03 2.14E-03 2.79E-02 6.40E-03 9.71E-02 2.13E-01 ±4.4

124.0 3.37E-03 2.25E-03 2.91E-02 6.72E-03 1.01E-01 2.21E-01 ±4.4

124.5 3.53E-03 2.36E-03 3.02E-02 7.05E-03 1.05E-01 2.30E-01 ±4.3

125.0 3.70E-03 2.47E-03 3.14E-02 7.38E-03 1.10E-01 2.40E-01 ±4.3

125.5 3.87E-03 2.58E-03 3.26E-02 7.73E-03 1.14E-01 2.49E-01 ±4.2

126.0 4.05E-03 2.70E-03 3.38E-02 8.08E-03 1.18E-01 2.59E-01 ±4.1

126.5 4.23E-03 2.82E-03 3.51E-02 8.44E-03 1.23E-01 2.68E-01 ±4.1

127.0 4.42E-03 2.94E-03 3.64E-02 8.81E-03 1.27E-01 2.78E-01 ±4.0

127.5 4.60E-03 3.07E-03 3.76E-02 9.18E-03 1.32E-01 2.89E-01 ±4.0

128.0 4.79E-03 3.20E-03 3.89E-02 9.56E-03 1.37E-01 2.99E-01 ±3.9

128.5 4.99E-03 3.32E-03 4.03E-02 9.94E-03 1.41E-01 3.09E-01 ±3.8

129.0 5.18E-03 3.46E-03 4.16E-02 1.03E-02 1.46E-01 3.20E-01 ±3.8

129.5 5.38E-03 3.59E-03 4.30E-02 1.07E-02 1.51E-01 3.30E-01 ±3.7

130.0 5.59E-03 3.72E-03 4.43E-02 1.11E-02 1.56E-01 3.41E-01 ±3.7

November 18, 2011 – 11 : 26 DRAFT 29

Table 21: SM Higgs branching ratios for the different four-fermion final states and their total uncertainties (ex-pressed in percentage). Low and intermediate mass range.




130.5 5.79E-03 3.86E-03 4.57E-02 1.15E-02 1.61E-01 3.52E-01 ±3.6

131.0 6.00E-03 4.00E-03 4.71E-02 1.20E-02 1.66E-01 3.63E-01 ±3.5

131.5 6.21E-03 4.14E-03 4.85E-02 1.24E-02 1.71E-01 3.74E-01 ±3.5

132.0 6.41E-03 4.28E-03 4.99E-02 1.28E-02 1.76E-01 3.85E-01 ±3.4

132.5 6.62E-03 4.42E-03 5.14E-02 1.32E-02 1.81E-01 3.96E-01 ±3.3

133.0 6.83E-03 4.56E-03 5.28E-02 1.36E-02 1.87E-01 4.08E-01 ±3.3

133.5 7.05E-03 4.70E-03 5.42E-02 1.40E-02 1.92E-01 4.19E-01 ±3.2

134.0 7.26E-03 4.84E-03 5.57E-02 1.45E-02 1.97E-01 4.31E-01 ±3.1

134.5 7.47E-03 4.98E-03 5.72E-02 1.49E-02 2.02E-01 4.42E-01 ±3.1

135.0 7.68E-03 5.12E-03 5.86E-02 1.53E-02 2.08E-01 4.53E-01 ±3.0

135.5 7.89E-03 5.26E-03 6.01E-02 1.57E-02 2.13E-01 4.65E-01 ±2.9

136.0 8.09E-03 5.39E-03 6.16E-02 1.61E-02 2.18E-01 4.76E-01 ±2.8

136.5 8.30E-03 5.53E-03 6.30E-02 1.65E-02 2.23E-01 4.88E-01 ±2.6

137.0 8.50E-03 5.67E-03 6.45E-02 1.69E-02 2.29E-01 4.99E-01 ±2.5

137.5 8.70E-03 5.80E-03 6.60E-02 1.73E-02 2.34E-01 5.11E-01 ±2.4

138.0 8.90E-03 5.93E-03 6.75E-02 1.77E-02 2.39E-01 5.22E-01 ±2.2

138.5 9.10E-03 6.06E-03 6.90E-02 1.81E-02 2.45E-01 5.34E-01 ±2.1

139.0 9.29E-03 6.19E-03 7.04E-02 1.85E-02 2.50E-01 5.45E-01 ±1.9

139.5 9.47E-03 6.31E-03 7.19E-02 1.89E-02 2.55E-01 5.57E-01 ±1.8

140.0 9.65E-03 6.44E-03 7.34E-02 1.92E-02 2.60E-01 5.68E-01 ±1.7

141.0 1.00E-02 6.67E-03 7.63E-02 1.99E-02 2.70E-01 5.91E-01 ±1.6

142.0 1.03E-02 6.89E-03 7.92E-02 2.06E-02 2.81E-01 6.13E-01 ±1.5

143.0 1.06E-02 7.08E-03 8.21E-02 2.11E-02 2.91E-01 6.35E-01 ±1.4

144.0 1.09E-02 7.26E-03 8.50E-02 2.17E-02 3.00E-01 6.56E-01 ±1.3

145.0 1.11E-02 7.42E-03 8.79E-02 2.21E-02 3.10E-01 6.77E-01 ±1.2

146.0 1.13E-02 7.55E-03 9.07E-02 2.25E-02 3.20E-01 6.98E-01 ±1.2

147.0 1.15E-02 7.65E-03 9.36E-02 2.28E-02 3.29E-01 7.19E-01 ±1.1

148.0 1.16E-02 7.71E-03 9.64E-02 2.30E-02 3.38E-01 7.39E-01 ±1.0

149.0 1.16E-02 7.74E-03 9.92E-02 2.31E-02 3.47E-01 7.58E-01 ±0.9

150.0 1.16E-02 7.73E-03 1.02E-01 2.31E-02 3.56E-01 7.77E-01 ±0.9

151.0 1.15E-02 7.68E-03 1.05E-01 2.29E-02 3.64E-01 7.96E-01 ±0.8

152.0 1.14E-02 7.57E-03 1.08E-01 2.26E-02 3.72E-01 8.14E-01 ±0.7

153.0 1.11E-02 7.41E-03 1.10E-01 2.21E-02 3.80E-01 8.32E-01 ±0.7

154.0 1.08E-02 7.18E-03 1.13E-01 2.14E-02 3.88E-01 8.49E-01 ±0.6

155.0 1.03E-02 6.88E-03 1.16E-01 2.05E-02 3.96E-01 8.67E-01 ±0.5

156.0 9.73E-03 6.49E-03 1.19E-01 1.94E-02 4.04E-01 8.84E-01 ±0.5

157.0 9.00E-03 6.00E-03 1.23E-01 1.79E-02 4.11E-01 9.01E-01 ±0.4

158.0 8.09E-03 5.39E-03 1.26E-01 1.61E-02 4.18E-01 9.17E-01 ±0.3

159.0 7.01E-03 4.68E-03 1.30E-01 1.39E-02 4.25E-01 9.33E-01 ±0.3

160.0 5.83E-03 3.88E-03 1.33E-01 1.16E-02 4.32E-01 9.49E-01 ±0.2

162.0 3.96E-03 2.64E-03 1.38E-01 7.88E-03 4.42E-01 9.70E-01 ±0.2

164.0 3.25E-03 2.17E-03 1.40E-01 6.47E-03 4.46E-01 9.79E-01 ±0.1

166.0 3.07E-03 2.04E-03 1.41E-01 6.11E-03 4.48E-01 9.84E-01 ±0.1

168.0 3.12E-03 2.08E-03 1.41E-01 6.21E-03 4.49E-01 9.86E-01 ±0.1

170.0 3.32E-03 2.21E-03 1.41E-01 6.61E-03 4.50E-01 9.88E-01 ±0.1

November 18, 2011 – 11 : 26 DRAFT 30

Table 22: SM Higgs branching ratios for the different four-fermion final states and their total uncertainties (ex-pressed in percentage). Intermediate mass range.




172.0 3.67E-03 2.44E-03 1.41E-01 7.30E-03 4.50E-01 9.89E-01 ±0.0

174.0 4.19E-03 2.79E-03 1.41E-01 8.34E-03 4.51E-01 9.90E-01 ±0.0

176.0 4.98E-03 3.32E-03 1.40E-01 9.92E-03 4.51E-01 9.91E-01 ±0.0

178.0 6.24E-03 4.16E-03 1.39E-01 1.24E-02 4.52E-01 9.91E-01 ±0.0

180.0 8.47E-03 5.65E-03 1.37E-01 1.69E-02 4.53E-01 9.92E-01 ±0.0

182.0 1.27E-02 8.44E-03 1.32E-01 2.52E-02 4.54E-01 9.93E-01 ±0.0

184.0 1.85E-02 1.23E-02 1.26E-01 3.69E-02 4.56E-01 9.93E-01 ±0.0

186.0 2.34E-02 1.56E-02 1.21E-01 4.66E-02 4.57E-01 9.94E-01 ±0.0

188.0 2.69E-02 1.79E-02 1.18E-01 5.36E-02 4.58E-01 9.94E-01 ±0.0

190.0 2.95E-02 1.97E-02 1.15E-01 5.87E-02 4.59E-01 9.95E-01 ±0.0

192.0 3.14E-02 2.09E-02 1.13E-01 6.26E-02 4.60E-01 9.95E-01 ±0.0

194.0 3.29E-02 2.20E-02 1.12E-01 6.56E-02 4.60E-01 9.95E-01 ±0.0

196.0 3.42E-02 2.28E-02 1.10E-01 6.80E-02 4.61E-01 9.96E-01 ±0.0

198.0 3.51E-02 2.34E-02 1.09E-01 7.00E-02 4.61E-01 9.96E-01 ±0.0

200.0 3.60E-02 2.40E-02 1.08E-01 7.16E-02 4.61E-01 9.96E-01 ±0.0

202.0 3.67E-02 2.44E-02 1.08E-01 7.30E-02 4.61E-01 9.96E-01 ±0.0

204.0 3.72E-02 2.48E-02 1.07E-01 7.42E-02 4.62E-01 9.96E-01 ±0.0

206.0 3.77E-02 2.52E-02 1.07E-01 7.52E-02 4.62E-01 9.96E-01 ±0.0

208.0 3.82E-02 2.55E-02 1.06E-01 7.61E-02 4.62E-01 9.97E-01 ±0.0

210.0 3.86E-02 2.57E-02 1.06E-01 7.68E-02 4.62E-01 9.97E-01 ±0.0

212.0 3.89E-02 2.59E-02 1.06E-01 7.75E-02 4.62E-01 9.97E-01 ±0.0

214.0 3.92E-02 2.61E-02 1.05E-01 7.81E-02 4.62E-01 9.97E-01 ±0.0

216.0 3.95E-02 2.63E-02 1.05E-01 7.86E-02 4.63E-01 9.97E-01 ±0.0

218.0 3.97E-02 2.65E-02 1.05E-01 7.91E-02 4.63E-01 9.97E-01 ±0.0

220.0 3.99E-02 2.66E-02 1.05E-01 7.95E-02 4.63E-01 9.97E-01 ±0.0

222.0 4.01E-02 2.67E-02 1.04E-01 7.99E-02 4.63E-01 9.97E-01 ±0.0

224.0 4.03E-02 2.69E-02 1.04E-01 8.02E-02 4.63E-01 9.97E-01 ±0.0

226.0 4.04E-02 2.70E-02 1.04E-01 8.06E-02 4.63E-01 9.97E-01 ±0.0

228.0 4.06E-02 2.71E-02 1.04E-01 8.09E-02 4.63E-01 9.97E-01 ±0.0

230.0 4.07E-02 2.72E-02 1.04E-01 8.12E-02 4.63E-01 9.98E-01 ±0.0

232.0 4.09E-02 2.73E-02 1.04E-01 8.14E-02 4.63E-01 9.98E-01 ±0.0

234.0 4.10E-02 2.73E-02 1.03E-01 8.17E-02 4.63E-01 9.98E-01 ±0.0

236.0 4.11E-02 2.74E-02 1.03E-01 8.19E-02 4.63E-01 9.98E-01 ±0.0

238.0 4.12E-02 2.75E-02 1.03E-01 8.21E-02 4.63E-01 9.98E-01 ±0.0

240.0 4.13E-02 2.76E-02 1.03E-01 8.23E-02 4.63E-01 9.98E-01 ±0.0

242.0 4.14E-02 2.76E-02 1.03E-01 8.25E-02 4.63E-01 9.98E-01 ±0.0

244.0 4.15E-02 2.77E-02 1.03E-01 8.27E-02 4.64E-01 9.98E-01 ±0.0

246.0 4.16E-02 2.77E-02 1.03E-01 8.29E-02 4.64E-01 9.98E-01 ±0.0

248.0 4.17E-02 2.78E-02 1.03E-01 8.30E-02 4.64E-01 9.98E-01 ±0.0

250.0 4.18E-02 2.78E-02 1.03E-01 8.32E-02 4.64E-01 9.98E-01 ±0.0

252.0 4.18E-02 2.79E-02 1.03E-01 8.34E-02 4.64E-01 9.98E-01 ±0.0

254.0 4.19E-02 2.79E-02 1.03E-01 8.35E-02 4.64E-01 9.98E-01 ±0.0

256.0 4.20E-02 2.80E-02 1.02E-01 8.37E-02 4.64E-01 9.98E-01 ±0.0

258.0 4.21E-02 2.80E-02 1.02E-01 8.38E-02 4.64E-01 9.98E-01 ±0.0

260.0 4.21E-02 2.81E-02 1.02E-01 8.39E-02 4.64E-01 9.98E-01 ±0.0

November 18, 2011 – 11 : 26 DRAFT 31

Table 23: SM Higgs branching ratios for the different four-fermion final states and their total uncertainties (ex-pressed in percentage). High mass range.




262.0 4.22E-02 2.81E-02 1.02E-01 8.41E-02 4.64E-01 9.98E-01 ±0.0

264.0 4.23E-02 2.82E-02 1.02E-01 8.42E-02 4.64E-01 9.98E-01 ±0.0

266.0 4.23E-02 2.82E-02 1.02E-01 8.43E-02 4.64E-01 9.98E-01 ±0.0

268.0 4.24E-02 2.83E-02 1.02E-01 8.44E-02 4.64E-01 9.98E-01 ±0.0

270.0 4.24E-02 2.83E-02 1.02E-01 8.45E-02 4.64E-01 9.98E-01 ±0.0

272.0 4.25E-02 2.83E-02 1.02E-01 8.47E-02 4.64E-01 9.98E-01 ±0.0

274.0 4.26E-02 2.84E-02 1.02E-01 8.48E-02 4.64E-01 9.98E-01 ±0.0

276.0 4.26E-02 2.84E-02 1.02E-01 8.49E-02 4.64E-01 9.98E-01 ±0.0

278.0 4.27E-02 2.84E-02 1.02E-01 8.50E-02 4.64E-01 9.98E-01 ±0.0

280.0 4.27E-02 2.85E-02 1.02E-01 8.51E-02 4.64E-01 9.98E-01 ±0.0

282.0 4.28E-02 2.85E-02 1.02E-01 8.52E-02 4.64E-01 9.98E-01 ±0.0

284.0 4.28E-02 2.85E-02 1.02E-01 8.53E-02 4.64E-01 9.98E-01 ±0.0

286.0 4.29E-02 2.86E-02 1.02E-01 8.54E-02 4.64E-01 9.98E-01 ±0.0

288.0 4.29E-02 2.86E-02 1.02E-01 8.55E-02 4.64E-01 9.98E-01 ±0.0

290.0 4.30E-02 2.86E-02 1.02E-01 8.56E-02 4.64E-01 9.98E-01 ±0.0

295.0 4.31E-02 2.87E-02 1.01E-01 8.58E-02 4.64E-01 9.98E-01 ±0.0

300.0 4.32E-02 2.88E-02 1.01E-01 8.60E-02 4.64E-01 9.99E-01 ±0.0

305.0 4.33E-02 2.88E-02 1.01E-01 8.62E-02 4.64E-01 9.99E-01 ±0.0

310.0 4.34E-02 2.89E-02 1.01E-01 8.64E-02 4.64E-01 9.99E-01 ±0.0

315.0 4.34E-02 2.90E-02 1.01E-01 8.66E-02 4.64E-01 9.99E-01 ±0.0

320.0 4.35E-02 2.90E-02 1.01E-01 8.67E-02 4.64E-01 9.98E-01 ±0.0

325.0 4.36E-02 2.91E-02 1.01E-01 8.68E-02 4.64E-01 9.98E-01 ±0.0

330.0 4.37E-02 2.91E-02 1.01E-01 8.70E-02 4.64E-01 9.98E-01 ±0.0

335.0 4.37E-02 2.91E-02 1.01E-01 8.71E-02 4.64E-01 9.98E-01 ±0.0

340.0 4.37E-02 2.92E-02 1.01E-01 8.72E-02 4.64E-01 9.98E-01 ±0.0

345.0 4.37E-02 2.91E-02 1.00E-01 8.71E-02 4.63E-01 9.95E-01 ±0.7

350.0 4.32E-02 2.88E-02 9.90E-02 8.61E-02 4.57E-01 9.83E-01 ±1.4

360.0 4.17E-02 2.78E-02 9.53E-02 8.31E-02 4.41E-01 9.47E-01 ±2.6

370.0 4.04E-02 2.69E-02 9.20E-02 8.05E-02 4.26E-01 9.15E-01 ±2.9

380.0 3.93E-02 2.62E-02 8.92E-02 7.84E-02 4.14E-01 8.89E-01 ±3.1

390.0 3.85E-02 2.57E-02 8.70E-02 7.67E-02 4.04E-01 8.68E-01 ±3.1

400.0 3.79E-02 2.52E-02 8.52E-02 7.54E-02 3.96E-01 8.51E-01 ±3.1

410.0 3.74E-02 2.49E-02 8.38E-02 7.44E-02 3.90E-01 8.38E-01 ±3.1

420.0 3.70E-02 2.47E-02 8.27E-02 7.37E-02 3.85E-01 8.28E-01 ±3.1

430.0 3.68E-02 2.45E-02 8.19E-02 7.32E-02 3.82E-01 8.20E-01 ±3.0

440.0 3.66E-02 2.44E-02 8.12E-02 7.29E-02 3.79E-01 8.15E-01 ±3.0

450.0 3.65E-02 2.44E-02 8.08E-02 7.27E-02 3.77E-01 8.11E-01 ±2.9

460.0 3.65E-02 2.43E-02 8.04E-02 7.27E-02 3.76E-01 8.08E-01 ±2.8

470.0 3.65E-02 2.43E-02 8.02E-02 7.27E-02 3.75E-01 8.07E-01 ±2.8

480.0 3.65E-02 2.44E-02 8.01E-02 7.28E-02 3.75E-01 8.06E-01 ±2.7

490.0 3.66E-02 2.44E-02 8.00E-02 7.29E-02 3.75E-01 8.06E-01 ±2.6

500.0 3.67E-02 2.45E-02 8.00E-02 7.31E-02 3.75E-01 8.07E-01 ±2.4

510.0 3.68E-02 2.46E-02 8.01E-02 7.33E-02 3.76E-01 8.08E-01 ±2.3

520.0 3.70E-02 2.47E-02 8.02E-02 7.36E-02 3.77E-01 8.10E-01 ±2.4

530.0 3.71E-02 2.48E-02 8.03E-02 7.39E-02 3.78E-01 8.12E-01 ±2.4

540.0 3.73E-02 2.49E-02 8.05E-02 7.42E-02 3.79E-01 8.14E-01 ±2.4

November 18, 2011 – 11 : 26 DRAFT 32

Table 24: SM Higgs branching ratios for the different four-fermion final states and their total uncertainties (ex-pressed in percentage). Very high mass range.




550.0 3.75E-02 2.50E-02 8.06E-02 7.45E-02 3.80E-01 8.16E-01 ±2.4

560.0 3.76E-02 2.51E-02 8.09E-02 7.49E-02 3.81E-01 8.19E-01 ±2.5

570.0 3.78E-02 2.52E-02 8.11E-02 7.52E-02 3.82E-01 8.22E-01 ±2.5

580.0 3.80E-02 2.53E-02 8.13E-02 7.56E-02 3.84E-01 8.25E-01 ±2.5

590.0 3.82E-02 2.54E-02 8.16E-02 7.60E-02 3.85E-01 8.28E-01 ±2.5

600.0 3.83E-02 2.56E-02 8.18E-02 7.63E-02 3.87E-01 8.31E-01 ±2.5

610.0 3.85E-02 2.57E-02 8.21E-02 7.67E-02 3.88E-01 8.34E-01 ±2.5

620.0 3.87E-02 2.58E-02 8.24E-02 7.70E-02 3.89E-01 8.37E-01 ±2.6

630.0 3.89E-02 2.59E-02 8.27E-02 7.74E-02 3.91E-01 8.40E-01 ±2.5

640.0 3.91E-02 2.61E-02 8.29E-02 7.78E-02 3.92E-01 8.43E-01 ±2.6

650.0 3.93E-02 2.62E-02 8.32E-02 7.81E-02 3.94E-01 8.46E-01 ±2.6

660.0 3.94E-02 2.63E-02 8.35E-02 7.85E-02 3.95E-01 8.50E-01 ±2.6

670.0 3.96E-02 2.64E-02 8.38E-02 7.88E-02 3.97E-01 8.53E-01 ±2.6

680.0 3.98E-02 2.65E-02 8.40E-02 7.92E-02 3.98E-01 8.56E-01 ±2.6

690.0 4.00E-02 2.66E-02 8.43E-02 7.95E-02 3.99E-01 8.59E-01 ±2.6

700.0 4.01E-02 2.68E-02 8.46E-02 7.98E-02 4.01E-01 8.62E-01 ±2.6

710.0 4.03E-02 2.69E-02 8.48E-02 8.02E-02 4.02E-01 8.65E-01 ±2.6

720.0 4.05E-02 2.70E-02 8.51E-02 8.05E-02 4.04E-01 8.68E-01 ±2.6

730.0 4.06E-02 2.71E-02 8.54E-02 8.08E-02 4.05E-01 8.71E-01 ±2.6

740.0 4.08E-02 2.72E-02 8.56E-02 8.11E-02 4.06E-01 8.74E-01 ±2.6

750.0 4.09E-02 2.73E-02 8.59E-02 8.14E-02 4.08E-01 8.76E-01 ±2.6

760.0 4.11E-02 2.74E-02 8.62E-02 8.17E-02 4.09E-01 8.79E-01 ±2.6

770.0 4.12E-02 2.75E-02 8.64E-02 8.20E-02 4.10E-01 8.82E-01 ±2.6

780.0 4.14E-02 2.76E-02 8.67E-02 8.23E-02 4.11E-01 8.85E-01 ±2.6

790.0 4.15E-02 2.77E-02 8.69E-02 8.26E-02 4.13E-01 8.87E-01 ±2.7

800.0 4.17E-02 2.78E-02 8.72E-02 8.29E-02 4.14E-01 8.90E-01 ±2.7

810.0 4.18E-02 2.79E-02 8.74E-02 8.31E-02 4.15E-01 8.93E-01 ±2.7

820.0 4.19E-02 2.80E-02 8.76E-02 8.34E-02 4.16E-01 8.95E-01 ±2.7

830.0 4.21E-02 2.80E-02 8.79E-02 8.37E-02 4.17E-01 8.98E-01 ±2.7

840.0 4.22E-02 2.81E-02 8.81E-02 8.39E-02 4.18E-01 9.00E-01 ±2.7

850.0 4.23E-02 2.82E-02 8.83E-02 8.42E-02 4.19E-01 9.02E-01 ±2.7

860.0 4.24E-02 2.83E-02 8.85E-02 8.44E-02 4.20E-01 9.05E-01 ±2.7

870.0 4.26E-02 2.84E-02 8.87E-02 8.46E-02 4.21E-01 9.07E-01 ±2.7

880.0 4.27E-02 2.85E-02 8.90E-02 8.49E-02 4.22E-01 9.09E-01 ±2.8

890.0 4.28E-02 2.85E-02 8.92E-02 8.51E-02 4.23E-01 9.11E-01 ±2.8

900.0 4.29E-02 2.86E-02 8.94E-02 8.53E-02 4.24E-01 9.13E-01 ±2.8

910.0 4.30E-02 2.87E-02 8.96E-02 8.55E-02 4.25E-01 9.16E-01 ±2.8

920.0 4.31E-02 2.88E-02 8.98E-02 8.57E-02 4.26E-01 9.18E-01 ±2.8

930.0 4.32E-02 2.88E-02 9.00E-02 8.59E-02 4.27E-01 9.20E-01 ±2.8

940.0 4.33E-02 2.89E-02 9.02E-02 8.62E-02 4.28E-01 9.22E-01 ±2.8

950.0 4.34E-02 2.90E-02 9.03E-02 8.64E-02 4.29E-01 9.24E-01 ±2.8

960.0 4.35E-02 2.90E-02 9.05E-02 8.65E-02 4.30E-01 9.25E-01 ±2.8

970.0 4.36E-02 2.91E-02 9.07E-02 8.67E-02 4.31E-01 9.27E-01 ±2.8

980.0 4.37E-02 2.92E-02 9.09E-02 8.69E-02 4.31E-01 9.29E-01 ±2.9

990.0 4.38E-02 2.92E-02 9.10E-02 8.71E-02 4.32E-01 9.31E-01 ±2.9

1000.0 4.39E-02 2.93E-02 9.12E-02 8.73E-02 4.33E-01 9.33E-01 ±2.9

November 18, 2011 – 11 : 26 DRAFT 33

2.2 MSSM Higgs branching ratios413

In the MSSM the evaluation of cross sections and of branchingratios have several common issues as414

outlined in Sect.??. It was discussed thatbeforeany branching ratio calculation can be performed in415

a first step the Higgs boson masses, couplings and mixings have to be evaluated from the underlying416

set of (soft SUSY-breaking) parameters. A brief comparisonof the dedicated codes that provide this417

kind of calculations (FEYNHIGGS [74–77] and CPSUPERH [78, 79]) was been given in Ref. [6], where418

it was concluded that in the case of real parameters more corrections are included into FEYNHIGGS.419

Consequently, FEYNHIGGS was chosen for the corresponding evaluations in this report. The results for420

Higgs boson masses and couplings can be provided to other codes (especially HDECAY [12–14]) via421

the SUSY Les Houches Accord [80,81].422

In the following subsections we describe how the relevant codes for the calculation of partial decay423

widths, FEYNHIGGS and HDECAY, are combined to give the most precise result for the Higgs-boson424

branching ratios in the MSSM. Numerical results are shown within themmaxh scenario [7], where it425

should be stressed that it would be desirable to interpret the model independent results of various Higgs-426

boson searches at the LHC also in other benchmark models, seefor instance Refs. [7,82]. We restrict the427

evaluation totan β = 1 . . . 60 andMA = 90 GeV. . . 500 GeV.428

2.2.1 Combination of calculations429

After the calculation of Higgs-boson masses and mixings from the original SUSY input the branching430

ratio calculation has to be performed. This can be done with the codes, CPSUPERH and FEYNHIGGS431

for real or complex parameters, or HDECAY for real parameters. The higher-order corrections included432

in the calculation of the various decay channels differ in the three codes.433

Here we concentrate on the MSSM with real parameters. We combine the results from HDECAY434

and FEYNHIGGS on various decay channels to obtain the most accurate resultfor the branching ratios435

currently available. In a first step, all partial widths havebeen calculated as accurately as possible. Then436

the branching ratios have been derived from this full set of partial widths. Concretely, we used FEYN-437

HIGGS for the evaluation of the Higgs boson masses and couplings from the original input parameters,438

including corrections up to the two-loop level. FEYNHIGGS results are furthermore used for the channels439

(φ = h,H,A),440

– Γ(H → τ+τ−): a full one-loop calculation of the decay width is included.441

– Γ(H → µ+µ−): a full one-loop calculation of the decay width is included.442

– Γ(H → V(∗)V(∗)), V =W±, Z: results for a SM Higgs boson, taken from PROPHECY4F [15–17]443

and based on a full one-loop calculation, are dressed with effective couplings for the respective444

coupling of the MSSM Higgs boson to SM gauge bosons, see Sect.??. It should be noted that this445

does not correspond to a full one-loop calculation in the MSSM, and the approximation may be446

insufficient for very low values ofMA.447

The results for the Higgs-boson masses and couplings are passed to HDECAY via the SUSY Les448

Houches Accord [80,81]. Using these results the following channels have been evaluated by HDECAY,449

– Γ(H → bb): SM QCD corrections are included up to the four-loop level; MSSM specific correc-450

tions, most notably entering via∆b have been included up to the leading two-loop corrections [83].451

– Γ(H → tt): HDECAY includes . . .452

– Γ(H → cc): HDECAY includes . . .453

– Γ(H → gg): HDECAY includes . . .454

– Γ(H → γγ): HDECAY includes . . .455

– Γ(H → Zγ): HDECAY includes . . .456

November 18, 2011 – 11 : 26 DRAFT 34

Other decay channels such asH → ss and the decays to lighter fermions are not included since457

they are neither relevant for LHC searches, nor do they contribute significantly to the total decay width.458

With future releases of FEYNHIGGS, HDECAY and other codes the evaluation of individual channels459

might change to another code.460

The total decay width is calculated as,

Γφ = ΓFHH→τ+τ− + ΓFH

H→µ+µ− + ΓFH/P4f

H→W(∗)W(∗) + ΓFH/P4f

H→Z(∗)Z(∗)

+ ΓHDH→bb + ΓHD

H→tt + ΓHDH→cc + ΓHD

H→gg + ΓHDH→γγ + ΓHD

H→Zγ , (6)

followed by a corresponding evaluation of the respective branching ratio. Decays to strange quarks or461

other ligher fermions have been neglected. Due to the somewhat different calculation compared to the462

SM case in Sect. 2.1.1 no full decoupling of the decay widths and branching ratios of the light MSSM463

Higgs to the respective SM values can be expected.464

2.2.2 Results in themmaxh

scenario465

The procedure outlined in the previous subsection can be applied to arbitrary points in the MSSM pa-466

rameter space. Here we show representative results in themmaxh scenario.467

→ one table similar to table 32 in YR1 for each channel:bb, ττ , µµ, γγ,WW , ZZ468

→ plots of BRs, in each plotMA is varied andtan β is fixed to 5, 10, 20, 30, 40, 50.469

November 18, 2011 – 11 : 26 DRAFT 35

3 Parton Distribution Functions5470

3.1 PDF Set Updates471

Several of the PDF sets which were discussed in the previous Yellow Report [6] have been updated472

since. NNPDF2.1 [84] is an updated version of NNPDF2.0 [85] which uses the FONLL general mass473

VFN scheme [86] instead of a zero mass scheme. There are also now NNPDF NNLO and LO sets [87],474

which are based on the same data and methodology as NNPDF2.1.The HERA PDF group now use475

HERAPDF1.5 [88], which contains more data than HERAPDF1.0 [89], a wider examination of param-476

eter dependence, and an NNLO set with uncertainty. This set is available in LHAPDF, however it is477

partially based on preliminary HERA-II structure functiondata.478

The current PDF4LHC prescription [90] for calculating a central value and uncertainty for a given479

process should undergo the simple modification of using the most up-to-date relevant set from the rele-480

vant group, i.e. NNPDF2.0 should be replaced with NNPDF2.1 [84] and CTEQ6.6 [91] with CT10 [92].481

3.2 Correlations482

The main aim of this section is to examine the correlations between different Higgs production processes483

and/or backgrounds to these processes. The PDF uncertaintyanalysis may be extended to define a484

correlation between the uncertainties of two variables, sayX(~a) andY (~a). As for the case of PDFs,485

the physical concept of PDF correlations can be determined both from PDF determinations based on486

the Hessian approach and on the Monte Carlo approach. For convenience and commonality, all physical487

processes were calculated using the MCFM NLO program (versions 5.8 and 6.0) [93,94] with a common488

set of input files for all groups.489

We present the results for the PDF correlations at NLO for Higgs production via gluon-gluon-490

fusion, vector boson fusion, in association withW or with att pair at massesMH = 120 GeV MH =491

160 GeV MH = 200 GeV MH = 300 GeV MH = 500 GeVWe also include a wide variety of492

background processes and other standard production mechanisms, i.e.W, WW, WZ, Wγ, Wbb, tt, tb493

and thet-channelt(→ b) + q, whereW denotes the average ofW+ andW−.494

For MSTW2008 [95], CT10 [92], GJR08 [96,97] and ABKM09 [98] PDFs the correlations of any495

two quantitiesX andY are calculated using the standard formula,496

ρ (X,Y ) ≡ cosϕ =

∑i(Xi −X0)(Yi − Y0)√∑

i(Xi −X0)2∑

i(Yi − Y0)2. (7)

The index in the sum runs over the number of free parameters and X0, Y0 correspond to the values497

obtained by the central PDF value. When positive and negative direction PDF eigenvectors are used this498

is equivalent to (see e.g. [91])499

cosϕ=~∆X ·~∆Y∆X∆Y

=1

4∆X∆Y

N∑

i=1

(X

(+)i −X(−)

i

)(Y

(+)i − Y

(−)i

), ∆X=

∣∣∣~∆X∣∣∣= 1

2

√√√√N∑

i=1

(X

(+)i −X(−)

i

)2,

(8)where the sum is over theN pairs of positive and negative PDF eigenvectors. For MSTW2008 and500

CT10 the eigenvectors by default contain only PDF parameters, andαs variation may be considered sep-501

arately. For GJR08 and ABKM09αs is one of the parameters used directly in calculating the correlation502

coefficient, with the central value and variation determined by the fit.503

Due to the specific error calculation prescription for HERAPDF1.5 which includes parameteriza-tion and model errors, the correlations can not be calculated in exactly the same way. Rather, a formula

5S. Forte, J. Huston and R. S. Thorne (eds); S. Alekhin, J. Blümlein, A.M. Cooper-Sarkar, S. Glazov, P. Jimenez-Delgado,S. Moch, P. Nadolsky, V. Radescu, J. Rojo, A. Sapronov, W.J. Stirling.

November 18, 2011 – 11 : 26 DRAFT 36

for uncertainty propagation can be used in which correlations can be expressed via relative errors ofcompounds and their combination:

σ2(

X

σ(X)+

Y

σ(Y )

)= 2 + 2 cosϕ, (9)

whereσ(O) is the PDF error of observableO calculated using the HERAPDF prescription.504

The correlations for the NNPDF prescription are calculatedas discussed in [99], namely505

ρ (X,Y ) =〈XY 〉rep − 〈X〉rep 〈Y 〉rep

σXσY(10)

where the averages are performed over theNrep = 100 replicas of the NNPDF2.1 set.506

For all sets the correlations are for the appropriate value of αs for the relevant PDF set.507

Table 25: The up-to-date PDF4LHC average for the correlations between all signal processes with other signaland background processes for Higgs production considered here. The processes have been classified in correlationclasses, as discussed in the text.

120 GeVggH VBF WH ttH

ggH 1 -0.6 -0.4 -0.2VBF -0.6 1 0.6 -0.4WH -0.2 0.6 1 -0.2ttH -0.2 -0.4 -0.2 1W -0.2 0.6 0.8 -0.6

WW -0.4 0.8 1 -0.2WZ -0.2 0.4 0.8 -0.4Wγ 0 0.6 0.8 -0.6Wbb -0.2 0.6 1 -0.2tt 0.2 -0.4 -0.4 1tb -0.4 0.6 1 -0.2

t(→ b)q 0.4 0 0 0


ggH 1 -0.6 -0.4 0.2VBF -0.6 1 0.6 -0.2WH -0.4 0.6 1 0ttH 0.2 -0.2 0 1W -0.4 0.4 0.6 -0.4

WW -0.4 0.6 0.8 -0.2WZ -0.4 0.4 0.8 -0.2Wγ -0.4 0.6 0.6 -0.6Wbb -0.2 0.6 0.8 -0.2tt 0.4 -0.4 -0.2 0.8tb -0.4 0.6 1 0

t(→ b)q 0.6 0 0 0


ggH 1 -0.6 -0.4 0.4VBF -0.6 1 0.4 -0.2WH -0.4 0.6 1 0ttH 0.4 -0.2 0 1W -0.6 0.4 0.6 -0.4

WW -0.4 0.6 0.8 -0.2WZ -0.4 0.4 0.8 -0.2Wγ -0.4 0.4 0.6 -0.6Wbb -0.2 0.6 0.8 -0.2tt 0.6 -0.4 -0.2 0.8tb -0.4 0.6 0.8 0

t(→ b)q 0.6 -0.2 0 0


ggH 1 -0.4 -0.2 0.6VBF -0.4 1 0.4 -0.2WH -0.2 0.4 1 0.2ttH 0.6 -0.2 0.2 1W -0.6 0.4 0.4 -0.6

WW -0.4 0.6 0.8 -0.2WZ -0.6 0.4 0.6 -0.4Wγ -0.6 0.4 0.4 -0.6Wbb -0.2 0.4 0.8 -0.2tt 1 -0.4 0 0.8tb -0.4 0.4 0.8 -0.2

t(→ b)q 0.4 -0.2 0 -0.2


ggH 1 -0.4 0 0.8VBF -0.4 1 0.4 -0.2WH 0 0.4 1 0ttH 0.8 -0.2 0 1W -0.6 0.4 0.2 -0.6

WW -0.4 0.6 0.6 -0.4WZ -0.6 0.4 0.6 -0.4Wγ -0.6 0.4 0.2 -0.6Wbb -0.4 0.4 0.6 -0.4tt 1 -0.4 0 0.8tb -0.4 0.4 0.8 -0.2

t(→ b)q 0.2 -0.2 0 -0.2

Table 26: The same as Table 25 for the correlations between backgroundprocesses.

W WW WZ Wγ Wbb tt tb t(→ b)q

W 1 0.8 0.8 1 0.6 -0.6 0.6 -0.2WW 0.8 1 0.8 0.8 0.8 -0.4 0.8 0WZ 0.8 0.8 1 0.8 0.8 -0.4 0.8 0Wγ 1 0.8 0.8 1 0.6 -0.4 0.8 0Wbb 0.6 0.8 0.8 0.6 1 -0.2 0.6 0tt -0.6 -0.4 -0.4 -0.6 -0.2 1 -0.4 0.2tb 0.6 0.8 0.8 0.8 0.6 -0.4 1 0.2

t(→ b)q -0.2 0 0 0 0 0.2 0.2 1

November 18, 2011 – 11 : 26 DRAFT 37

3.3 Results for the correlation study508

Our main result is the computation of the correlation between physical processes relevant to Higgs pro-509

duction, either as signal or as background. It is summarisedin Tables 25 and 26, where we show the510

PDF4LHC average for each of the correlations between signaland background processes considered.511

These tables classify each correlation in classes with∆ρ = 0.2, that is, if the correlation is1 ≥ ρ ≥ 0.9512

the processes is assigned correlation 1, if0.9 ≥ ρ ≥ 0.7 the processes is assigned correlation 0.8 and so513

on. The class width is typical of the spread of the results from the PDF sets, which are in generally very514

good, but not perfect agreement. The average is obtained using the most up-to-date PDF sets (CT10,515

MSTW08, NNPDF2.1) in the PDF4LHC recommendation, and it is appropriate for use in conjunction516

with the cross section results obtained in [6], and with the background processes listed; the change of517

correlations due to updating the prescription is insignificant in comparison to the class width.518

We have also compared this PDF4LHC average to the average using all six PDF sets. In general519

there is rather little change. There are quite a few cases where the average moves into a neighbouring520

class but in many cases due to a very small change taking the average just over a boundary between two521

classes. There is only a move into the next-to-neighbouringclass in a very small number of cases. For522

the VBF-Wγ correlation atMH = 120, 160 GeV it reduces from 0.6 to 0.2, for the VBF-W correlation523

atMH = 500 GeV it reduces from 0.4 to 0, for theWγ-tb correlation it reduces from 0.8 to 0.4, for524

WZ-ttH atMH = 120 GeV it increases from−0.4 to 0.0, and forWbb-ttH atMH = 200 GeV it525

increases from−0.2 to 0.2.526

-1

-0.5

0

0.5

1

Cor

rela

tion

with

W

LHC HiggsXSWG 2011

NNPDF2.1 CT10 MSTW08 PDF4LHC av

W WW WZ Wγ Wbb tt tb t(->b)q

-1

-0.5

0

0.5

1

Cor

rela

tion

with

W

LHC HiggsXSWG 2011

HERAPDF1.5 GJR08 ABKM09 PDF4LHC av


Fig. 5: The correlations betweenW production and the other background processes considered.We show theresults for NNPDF2.1, CT10 and MSTW2008 in the left plot, andHERAPDF, JR and ABKM in the right plot. Inboth cases we show the up-to-date PDF4LHC average result.

A more complete list of processes, with results for each individual PDF set, may be found in527

the tables on the webpage at the Higgs xsec TWiki [100]. Note however that there is a high degree528

of redundancy in the approximate correlations of many processes. For exampleW production is very529

similar toZ production, both depending on partons (quarks in this case)at very similar hard scales and530

x values. Similarly forWW andZZ, and the subprocessesgg → WW(ZZ) and Higgs production via531

gluon-gluon fusion forMH = 200 GeV.532

More detailed results are presented for the MSTW2008, NNPDF2.1, CT10, HERAPDF1.5, GJR08533

and ABKM09 PDFs in Figs. 5–16. The result using each individual PDF sets is compared to the (up-534

dated) PDF4LHC average. There is usually a fairly narrow clustering of the individual results about the535

average, with a small number of cases where there is one, or perhaps two outliers. The sets with the536

largest parameterisations for the PDFs generally tend to give smaller magnitude correlations or anticor-537

relations, but this is not always the case, e.g. NNPDF2.1 gives the largest anti-correlation for VBF-ttH.538

There are some unusual features, e.g. for HERAPDF1.5 and high values ofMH the ttH correlations539

November 18, 2011 – 11 : 26 DRAFT 38

-1

-0.5

0

0.5

1

Cor

rela

tion

with

WW

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

WW

LHC HiggsXSWG 2011



Fig. 6: The same as Fig. 5 forWW production.

-1

-0.5

0

0.5

1

Cor

rela

tion

with

WZ

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

WZ

LHC HiggsXSWG 2011



Fig. 7: The same as Fig. 5 forWZ production.

-1

-0.5

0

0.5

1

Cor

rela

tion

with

Wγ

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

Wγ

LHC HiggsXSWG 2011



Fig. 8: The same as Fig. 5 forWγ production.

with quantities depending on the high-x gluon, e.g. ggH and tt is opposite to the other sets and the540

correlations with quantities depending on high-x quarks and antiquarks, e.g. VBF andWW is stronger.541

This is possibly related to the large high-x antiquark distribution in HERAPDF which contributes tottH542

but notggH or very much tott. GJR08 has a tendency to obtain more correlation between some gluon543

dominated processes, e.g.ggH andtt and quark dominated processes, e.g.W andWZ, perhaps because544

November 18, 2011 – 11 : 26 DRAFT 39

-1

-0.5

0

0.5

1

Cor

rela

tion

with

Wbb

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

Wbb

LHC HiggsXSWG 2011



Fig. 9: The same as Fig. 5 forWbb production.

-1

-0.5

0

0.5

1

Cor

rela

tion

with

ttba

r

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

ttba

r

LHC HiggsXSWG 2011



Fig. 10: The same as Fig. 5 fortt production.

the dynamical generation of PDFs couples the gluon and quarkmore strongly.545

We can now also see the origin of the cases where the averages move two classes. For VBF-Wγ at546

lower masses GJR08, ABKM09 and HERAPDF1.5 all lie lower thanthe (updated) PDF4LHC average,547

but not too different to CT10. For VBF-W at MH = 500 GeV, ABKM09 and GJR08 give a small548

anticorrelation, while others give a correlation, though it is only large in the case of MSTW2008. For549

Wγ-tb the change is due to slightly lower correlations for GJR08. However, although the change is two550

classes, in practice it is barely more than 0.2. ForWZ-ttH atMH = 120 GeV both HERAPDF1.5 and551

GJR08 have a larger correlation. This increases withMH for HERAPDF1.5 as noted, whereas GJR08552

heads closer to the average, but the move atMH = 120 GeV is only marginally two classes, and is only553

one class for other masses. ForWbb-ttH atMH = 200 GeV the situation is similar, and MSTW2008554

gives easily the biggest pull in the direction of anticorrelation.555

3.4 Additional correlation studies556

The inclusion of theαs uncertainty on the correlations, compared to PDF only variation, was also studied557

for some PDF sets, e.g. MSTW2008 using the approximation that the PDF sets for the upper and lower558

αs values [101] simply form another pair of orthogonal eigenvectors (show to be true in the quadratic559

approximation in [102]). This can increase the correlationbetween some processes, i.e.W production560

and Higgs via gluon fusion, because the former increases with αs due to increased evolution of quarks561

while the latter increases due to direct dependence onαs. Similarly for e.g. Higgs production via gluon562

November 18, 2011 – 11 : 26 DRAFT 40

-1

-0.5

0

0.5

1

Cor

rela

tion

with

tb

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

tb

LHC HiggsXSWG 2011



Fig. 11: The same as Fig. 5 fortb production.

-1

-0.5

0

0.5

1

Cor

rela

tion

with

t(->

b)q

LHC HiggsXSWG 2011



-1

-0.5

0

0.5

1

Cor

rela

tion

with

tbq

LHC HiggsXSWG 2011


W WW WZ Wγ Wbb tt tb tbq

Fig. 12: The same as Fig. 5 fort-channelt(→ b)q production.

fusion andtt production since each depends directly onαs. This may also contribute to some of the563

stronger correlations seen using GJR08 in some similar cases. In a handful of processes it can reduce564

correlation, e.g.W andWbb since the latter has a much strongerαs dependence. In most cases the565

change compared to PDF-only correlation for a given PDF setsis of order 0.1-0.2, and it is not an566

obvious contributing factor to the cases where the (updated) PDF4LHC average is noticeably different567

to the average using six sets, except possibly toWbb-ttH atMH = 200 GeV, whereαs does increase568

correlation.569

A small number of correlations were also calculated at NNLO for MSTW2008 PDFs, i.e.W, Z570

andgg → H for the same range ofMH . The correlations when taking into account PDF uncertainty571

alone were almost identical to those at NLO, variations being less than0.05. Whenαs uncertainty was572

included the correlations changed a little more due togg → H having more direct dependence onαs,573

but this is a relatively minor effect. Certainly the resultsin Tables 25 and 26, though calculated at NLO,574

can be used with confidence at NNLO.575

November 18, 2011 – 11 : 26 DRAFT 41

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ggF

MH ( GeV )

Vector Boson Fusion

LHC HiggsXSWG 2011

NNPDF2.1CT10

MSTW08PDF4LHC Average

HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500MH ( GeV )

WH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500MH ( GeV )

ttH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ggF

MH ( GeV )

W

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500MH ( GeV )

WW

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500MH ( GeV )

WZ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ggF

MH ( GeV )

Wγ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

Wbb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

tt

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ggF

MH ( GeV )

tb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

t(->b)q

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

Fig. 13: Correlation between the gluon fusiongg → H process and the other signal and background processes asa function ofMH . We show the results for the individual PDF sets as well as theup-to-date PDF4LHC average.

November 18, 2011 – 11 : 26 DRAFT 42

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

Gluon-gluon Fusion

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

ttH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

W

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WW

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WZ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

Wγ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

Wbb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

tt

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

VB

F

MH ( GeV )

tb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

t(-> b)q

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

Fig. 14: The same as Fig. 13 for the vector boson fusion process.

November 18, 2011 – 11 : 26 DRAFT 43

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

WH

MH ( GeV )

Gluon-gluon Fusion

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

VBF

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

ttH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

WH

MH ( GeV )

W

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WW

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WZ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

WH

MH ( GeV )

Wγ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

Wbb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

tt

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

WH

MH ( GeV )

tb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

t(-> b)q

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

Fig. 15: The same as Fig. 13 for theWH production process.

November 18, 2011 – 11 : 26 DRAFT 44

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ttH

MH ( GeV )

Gluon-gluon Fusion

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

VBF

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WH

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ttH

MH ( GeV )

W

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WW

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

WZ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ttH

MH ( GeV )

Wγ

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

Wbb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

tt

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

Cor

rela

tion

with

ttH

MH ( GeV )

tb

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

-1

-0.5

0

0.5

1

120 160 200 300 500

MH ( GeV )

t(-> b)q

LHC HiggsXSWG 2011

NNPDF2.1CT10


HERAPDF1.5GJR08

ABKM09

Fig. 16: The same as Fig. 13 for thettH production process.

November 18, 2011 – 11 : 26 DRAFT 45

4 NLO Parton Shower 6576

4.1 Introduction577

4.2 Uncertainties in NLO+PS results578

Several uncertainties affect the NLO+PS results. We have579

– Factorization and renormalization scale uncertainties.Normally, the NLO calculation underlying580

the NLO+PS generator has independent factorization and renormalization scales, and the output581

of the generator is affected at the NNLO level if these scalesare varied.582

– Uncertainties related to the part of the real cross sectionthat is treated with the Shower Algorithm.583

– Uncertainties related to how the Shower Algorithm is implemented.584

– Uncertainties related to the use of PDF’s, i.e. whether thePDF’s used in the shower algorithm are585

different from those used in the NLO calculation.586

– Further uncertainties common to all Shower generators, i.e. hadronization, underlying event, etc.587

We focus here upon the first three items, that are by far the dominant ones. We deal, in the following, with588

the transverse momentum distribution of the Higgs boson, inthe processgg → H. For this distribution589

the NLO+PS results displays more marked differences with respect to the pure NLO calculation. The590

latter, in fact, is divergent forpT → 0, with and infinite negative spike atpT = 0, representing the con-591

tribution of the virtual corrections. The NLO+PS approaches, instead, yield a positive cross section for592

all pT , with the characteristic Sudakov peak at smallpT . Furthermore, this distribution can be computed593

(using the HqT program [103]) at a matched NNLL+NNLO accuracy, that can serve as a benchmark to594

characterize the output of the NLO+PS generators.595

We begin by showing in fig. 17 the comparisons of MCatNLO+HERWIG and POWHEG with596

HqT, with a choice of parameters that yields the best agreement, in shape, of the distributions. This597

choice of parameter is therefore the outcome of this study, in the sense that we recommend that the two598

programs should be run with these choices of parameter. Details of this recommendation will be given599

in the conclusion of this subsection. In the figures, the uncertainty band of the MCatNLO+HERWIG

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) MCatNLO-HW

HqT

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) POWHEG-PY

HqT

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

Fig. 17: Uncertainty bands for the transverse momentum spectrum of the Higgs boson at LHC, 7 TeV, for ahiggs massmH = 120GeV. On the left, the MCatNLO+HERWIG result obtained using the non-default value ofthe reference scale equal toMH . On the right, the POWHEG+PYTHIA output, using the non-default Rs + Rf

separation. The uncertainty bands are obtained by changingµR andµF by a factor of two above and below thecentral value, taken equal toMH , with the restriction0.5 < µR/µF < 2.

600

and of POWHEG+PYTHIA, both compared to the HqT uncertainty band, are displayed. In the lower601

insert in the figure, the ratio to the central value of HqT is also displayed. The two programs are run with602

6M. Felcini, F. Krauss, F. Maltoni, P. Nason and J. Yu.

November 18, 2011 – 11 : 26 DRAFT 46

the following non-default value of parameters: MCatNLO+HERWIG is run with the central value of the603

renormalization scale fixed toMH , and POWHEG is run turning on the feature that separates a finite604

part from the real cross section. The red, solid curves represent the uncertainty band of the NLO+PS,605

while the dotted blue lines represent the band obtained withthe HqT program. The reference scale is606

chosen equal toMH in HqT, and the scale variations are performed in the same wayas in the NLO+PS607

generators: once considers all variations of a factor of twoabove and below the central scale, with the608

restriction0.5 < µR/µF < 2. We have used the MSTW2008 NNLO central set for all curves. This is609

because HqT requires NNLO parton densities, and because we want to focus upon differences that have610

to do with the calculation itself, rather than the PDF’s. TheHqT result has been obtained by running611

the program with full NNLL+NNLO accuracy, using the “switched” result. The resummation scaleQ in612

HqT has been set toMH613

We notice that both programs are compatible in shape with theHqT prediction. We also notice614

that the error band of the two NLO+PS generators is relatively small at smallpT and becomes larger at615

largerpT . This should remind us that the NLO+PS prediction for the high pT tail is in fact a tree level616

only prediction, since the production of a Higgs plus a lightparton starts at orderα3s , its scale variation617

is of orderα4s , and itsrelative scale variation is of orderα4

s /α3s , i.e. of orderαs.7 On the other hand618

the total integral of the curve, i.e. the total cross section, and in fact also the Higgs rapidity distribution,619

that are obtained by integrating over all transverse momenta, are given by a term of orderα2s plus a term620

of orderα3s , and their scale variation is also of orderα4

s . Thus, their relative scale variation is of order621

α4s /α

2s , i.e.α2

s .622

It is instructive to analize the difference between MCatNLOand POWHEG at their default value of623

parameters. This is illustrated in fig. 18. The two program are in reasonable agreement at small transverse

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) MCatNLO-HW

HqT

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) POWHEG-PY

HqT

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

Fig. 18: The transverse momentum spectrum of the Higgs in MCatNLO (left) and in POWHEG+PYTHIA (right)compared to the HqT result. In the lower insert, the same results normalized to the HqT central value are shown.

624

momentum, but display a large difference (about a factor of 3) in the high transverse momentum tail.625

This difference has two causes. One is the different scale choice in MCatNLO, where by defaultµ =626

mT =√M2

H + p2T , wherepT is the transverse momentum of the Higgs. That accounts for a factor627

of (αs(mT )/αs(MH))3, which leads to a factor of roughly 1.6 for the last bin in the plots. (looking628

at the left plot of fig. 17, we see in fact that the MCatNLO result in the last bin is higher by about a629

factor of 1.6 with respect to fig. 18). The remaining difference is due to the fact that in POWHEG, used630

with standard parameter, the NLO K-factor multiplies the full transverse momentum distribution. The631

POWHEG output is thus similar to what is obtained with NLO+PSgenerator, as already observed in the632

first volume of this report.633

7Here we remind the reader thatµ2F

d

dµ2F

α3s (µR) = −b03α

4s (µR).

November 18, 2011 – 11 : 26 DRAFT 47

This point deserves a more detailed explanation, which can be given along the lines of refs. [104,634

105]. We write below the differential cross section for the hardest emission in NLO+PS implementations635

(see the first volume of this report for details)636

dσNLO+PS = dΦBBs(ΦB)

[∆s(pmin

⊥ ) + dΦR|BRs(ΦR)

B(ΦB)∆s(pT(Φ))

]+ dΦRR

f (ΦR), (11)

where637

Bs = B(ΦB) +

[V (ΦB) +

∫dΦR|BR

s(ΦR|B)

]. (12)

The sumRs + Rf yields the real cross section forgg → Hg, and the analogous terms for quark guon638

and quark-antiquark annihilation.639

In MCatNLO, theRs term is the Shower approximation to the real cross section, and it depends640

upon the SMC that is being used in conjunction with it. In POWHEG, one has much freedom in choosing641

Rs, with the only constraintRs ≤ R, in order to avoid negative weights, and provided that in thesmall642

transverse momentum limit it coincides withR.643

For the purpose of this review, we now S events (for Shower) those generated by the first term on644

the r.h.s. of 11, i.e. those generated using the Shower algorithm, and F (for finite) events those generated645

by theRf term.8 The scale dependence typically affects theB and theRf terms in a different way.646

A scale variation in the square bracket on the r.h.s. of eq. 11is in practice never performed, since in647

MCatNLO this can only be achieved by changing the scale in theMonte Carlo event generator that is648

being used, and in POWHEG the most straightforward way to perform it (i.e. varying it naively by a649

constant factor) would spoil the NLL accuracy of the Sudakovform factor. We thus assume from now650

on that the scales in the square parenthesis are kept fixed. Scale variation will thus affectBs andRf .651

We observe now that the shape of the transverse momentum of the hardest radiation in S events is652

not affected by scale variations, given that the square bracket on the r.h.s. of eq. 11 is not affected by it,653

and that the factorB is pT independent. From this, it immediately follows that the scale variation of the654

large transverse momentum tail of the spectrum is of relative orderα2s , i.e. the same relative order of the655

inclusive cross section, rather than of relative orderαs, sinceB is a quantity integrated in the transverse656

momentum. Eq. (11), in the large transverse momentum tail, becomes657

dσNLO+PS ≈ dΦBBs(ΦB)dΦR|B

Rs(ΦR)

B(ΦB)+ dΦRR

f (ΦR), (13)

From this equation we see that for large transverse momentum, the S event contribution to the cross658

section is enhanced by a factorB/B, which is in essence the K factor of the process. We wish to659

emphasize that this factor does not spoil the NLO accuracy ofthe result, since it affects the distribution660

by terms of higher order inαs. Now, in POWHEG, in its default configuration,Rf is only given by661

the tiny contributionqq → Hg, which is non-singular, so that S events dominate the cross section. The662

whole transverse momentum distribution is thus affected bythe K factor, yielding a result that is similar663

to what is obtained in ME+PS calculations, where the NLO K factor is applied to the LO distributions.664

Notice also that changing the form of the central value of thescales again does not change the transverse665

momentum distribution, that can only be affected by touching the scales in the Sudakov form factor.666

A simple approach to give a realistic assessment of the uncertainties in POWHEG, is to also exploit667

the freedom in the separationR = Rs+Rf . Besides the default valueRf = 0, one can also perform the668

separation669

Rs =h2

h2 + p2TR , Rf =

p2Th2 + p2T

R . (14)

8In the MCatNLO language, these are called S and H events, where S stands for soft, and H for hard. This reflects the factthat, in MC@NLO,Rs is in fact much softer thanRf .

November 18, 2011 – 11 : 26 DRAFT 48

In this way, S and F events are generated, with the former dominating the regionpT < h and the latter the670

regionpT > h. Notice that by sendingh to infinity one recovers the default behaviour. It is interesting671

to ask what happens ifh is made vanishingly small. It is easy to guess that in this limit the POWHEG672

results will end up coinciding with the pure NLO result. The freedom in the choice ofh, and also the673

freedom in changing the form of the separation in eq. 14 can beexploited to explore further uncertainties674

in POWHEG. The Sudakov exponent changes by terms subleadingin p2T , and so we can explore in this675

way uncertainties related to the shape of the Sudakov region. Furthermore, by suppressingRs at largepT676

the hard tail of the transverse momentum distribution becomes more sensitive to the scale choice. A new677

feature under study in the POWHEG BOX implements this choiceautomatically, on an event by event678

basis.9 The right plot of fig. 17 displays the POWHEG result obtained by implementing this feature.679

Notice that in this way the large transverse momentum tail becomes very similar to the MCatNLO result.680

The shape of the distribution at smaller transverse momentais also altered, and in better agreement with681

HqT. If mT rather thanMH is chosen as reference value for the scale, we obtain the result of fig. 19,682

where we see also here a fall of the cross section at large transverse momentum.

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) POWHEG-PY

HqT

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

Fig. 19: The transverse momentum spectrum of the Higgs in POWHEG+PYTHIA, using the separation os S andF events. The central scale is chosen equal to

√p2T +M2

H .

683

The shape of thepT distribution in MCatNLO+HW is not much affected by the change of scale684

for pT ≤ 100GeV . This is due to the fact that this region is dominated by S events. It is interesting685

to ask whether this region is affected if one changes the underlying Shower Monte Carlo generator. In686

MCatNLO, an interface to PYTHIA, using the virtuality ordered shower, is also available [106]. The687

results are displayed in fig. 20 We observe the following. Thelarge transverse momentum tails are688

consistent with the HERWIG version. We expect that since this region is dominated by F events. The689

shape of the Sudakov region has changed, showing a behaviourthat is more consistent with the HqT690

central value, down to scales of about 30 GeV. Below this scale, we observe a 50% increase of the cross691

section as smallerpT values are reached. This feature may be related to the choiceof the strong coupling692

scaleΛ in the Sudakov form factor, that both in POWHEG and in HERWIG is performed according to693

ref. [107]. A different choice is used in the virtuality ordered version of PYTHIA.694

Summarizing, we find large uncertainties in both MCatNLO andPOWHEG NLO+PS generators695

for Higgs production in gluon fusion. We have explored here uncertainties having to do with scale696

variation and to the separation of S and F events. If a higher accuracy result (namely HqT) was not697

available, the whole envelope of the uncertainties within each approach should be considered. These698

large uncertainties are all a direct consequence of the large NLO K-factor of thegg → H process. In699

spite of this fact, we have seen that there are choices of scales and parameters that bring the NLO+PS700

9The value ofh is chosen in such a way that the leading-log, approximate expression of the Sudakov form factor evaluatedath is equal to 0.99.

November 18, 2011 – 11 : 26 DRAFT 49

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) MCATNLO-py

HqT

00.5

11.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

10-4

10-3

10-2

0.1

1

dσ/d

pT (

pb/G

eV) MCATNLO-py

HqT

00.5

11.5

0 50 100 150 200 250 300 350 400

ratio

to H

qT

pT (GeV)

Fig. 20: The transverse momentum spectrum of the Higgs in MCatNLO+PYTHIA. The central scale is chosenequal toMH in the left plot, and to

√p2T +M2

H in the right plot.

results close in shape to the higher accuracy calculation ofthe transverse momentum spectrum provided701

by theHqT program. It is thus advisable to perform a choice of parameters that brings these generators702

in better agreement with HqT.703

4.2.1 Guidelines for estimating the uncertainty band with NLO+PS programs704

We thus give the following guideline for using the MCatNLO and POWHEG generators for Higgs pro-705

duction. In the MCatNLO case, we recommend to use the reference factorization and renormalization706

scale equal toMH rather thanmT . In POWHEG, we recommend using theRs/Rf separation. At the707

central value of the predictions, the ratioKHqT of the HqT over the NLO+PS and HqT cross section708

should be determined. The uncertainty bands are obtained byvarying the factorization and renormaliza-709

tion scale by a factor of 2 above and below the reference value, with the restriction0.5 < µF/µR < 2.710

All results shoud be multiplied byKHqT. In the MCatNLO case, this is the HERWIG result, with the711

central value of the scale taken equal toMH , while in POWHEG this is the result obtained with the S/F712

separation, (with the default central scale equal toMH ). Both results should be rescaled to the NNLO713

total cross section.714

4.2.2 Scale and PDF uncertainties in MCatNLO715

Fabio o Paolo, qui fate voi;716

4.2.3 Higgs production via gluon fusion in thePOWHEG approach in the SM and in the MSSM717

The implementation of the Higgs production process via gluon fusion in the current public release of718

POWHEG, described in Ref. [104], is based on matrix elements evaluated in the Heavy Quark Effective719

Theory (HQET). It also gives the user the possibility of rescaling the total cross section by a normaliza-720

tion factor, defined as the ratio between the exact Born contribution where the full dependence on the top721

and bottom masses is kept into account and the Born contribution evaluated in the HQET.722

Recently Ref. [108] presented an upgraded version of the code that allows to compute the gluon fu-723

sion cross section in the SM and in the MSSM. The SM simulationis based on matrix elements evaluated724

retaining the exact top and bottom mass dependence at NLO-QCD and NLO-EW. The MSSM simulation725

is based on matrix elements in which the exact dependence on the masses of quarks, squarks and Higgs726

boson has been retained in the LO amplitude, in the one-loop diagrams with real-parton emission and in727

the two-loop diagrams with quarks and gluons, whereas the approximation of vanishing Higgs mass has728

been employed in the two-loop diagrams involving superpartners. The leading NLO-EW effects have729

November 18, 2011 – 11 : 26 DRAFT 50

also been included in the evaluation of the matrix elements.Results obtained with this new version of730

POWHEG are presented in the SM??and in the MSSM?? sections of this Report.731

The code provides a complete description of on-shell Higgs production, including NLO-QCD732

corrections matched with a QCD parton shower and NLO-EW corrections. In the examples discussed733

in Ref. [108], the combinationPOWHEG + PYTHIA has been considered. In the MSSM case, the relevant734

parameters of the MSSM Lagrangian can be passed to the code via a Susy Les Houches Accord spectrum735

file.736

The code is available from the authors upon request. A release of the code that includes all the737

Higgs decay channels is in preparation.738

4.3 Uncertainties ingg → H → WW(∗)739

In this section a wide variety of different physics effects and uncertainties related to key observables in740

the processgg → H →W+W− → µ+νµe−νe is presented; they include741

– an appraisal of NLO matching methods, including a comparison with HNNLO [109] for some742

observables on the parton level;743

– perturbative uncertainties, like the impact of scale and PDF variations;744

– the impact of parton showering and non-perturbative effects on parton-level results; and745

– non-perturbative uncertainties, and in particular the impact of fragmentation variations and the746

effect of the underlying event and changes in its simulation.747

4.3.1 Setup748

In the following sections the SHERPA event generator [110] has been used in two modes: Matched749

samples have been produced according to the POWHEG [111, 112] and MC@NLO [113] methods,750

implemented as described in [114] and [115], respectively.Unless stated otherwise,mH = 160 GeV751

and the following cuts have been applied to leptons (ℓ = e, µ) and jetsj:752

– leptons:p(ℓ)⊥ ≥ 15 GeV and|η(ℓ)| ≤ 2.5|753

– jets (defined by the anti-kt algorithm [116] withR = 0.4): p(j)⊥ ≥ 25 GeV, |η(j)| ≤ 4.5.754

By default, for purely perturbative studies, the central PDF from the MSTW08 NLO set [95] has been755

used, while for those plots involving non-perturbative effects such as hadronisation and the underlying756

event, the central set of CT10 NLO [92] has been employed, since SHERPA has been tuned to jet data757

with this set. In both cases, the PDF set also fixes the strong coupling constant and its running behaviour758

in both matrix element and parton shower, and in the underlying event.759

4.3.2 Algorithmic dependence:POWHEG vs.MC@NLO760

Before embarking in this discussion, a number of points needto be stressed:761

1. The findings presented here are very recent, and they are partially at odds with previous con-762

clusions. So they should be understood as contributions to an ongoing discussion and hopefully763

trigger further work;764

2. clearly the issue of scales and, in particular, of resummation scales tends to be tricky. By far and765

large, however, the community agrees that the correct choice of resummation scaleQ is of the766

order of the factorisation scale, in the case at hand here, thereforeQ = O(mH). It is notoriously767

cumbersome to directly translate analytic resummation andscale choices there to parton shower768

programs;769

November 18, 2011 – 11 : 26 DRAFT 51

HNNLO

Sherpa NLO

Sherpa POWHEG

Sherpa MC@NLO α = 1

Sherpa MC@NLO α = 0.03

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.60.8

11.21.41.61.8

2

pT(H) [GeV]

Ratiowrt.HNNLO

HNNLO

Sherpa NLO

Sherpa POWHEG



5

10

15

20

25

30

35

σ(N

jet)[fb]

0 1 2

0.60.8

11.21.41.61.8

2

Njet

Ratiowrt.HNNLO

Fig. 21: The Higgs transverse momentum in all events (left) and the jet multiplicities (right) in pp → h →e−µ+νeνµ production. Here different approaches are compared with each other: two fixed order parton-levelcalculations at NNLO (HNNLO, black solid) and NLO (black, dashed), and three matched results in the SHERPA

implementations (POWHEG, blue and MC@NLO with α = 1, red dashed and withα = 0.03, red solid). Theyellow uncertainty band is given by the scale uncertaintiesof HNNLO.

3. the version of the MC@NLO algorithm presented here differs in some aspects from the version770

implemented in the original MC@NLO program; there, typically the HERWIG parton shower is771

being used, guaranteeing an upper limitation in the resummed phase space given by the factorisa-772

tion scale, and the FKS method [117] is used for the infrared subtraction on the matrix element773

level, the difference is compensated by a suitable correction term. In contrast, here, SHERPA is774

used, where both the parton shower and the infrared subtraction rely on Catani-Seymour subtrac-775

tion [118, 119], and the phase space limitation in the resummation bit is varied through a suitable776

parameter [120]α ∈ [0, 1], with α = 1 relating to no phase space restriction. We will indicate the777

choice ofα by a superscript. However, the results shown here should serve as an example only.778

Starting with a comparison at the matrix element level, consider Fig. 4.3.2, where results from779

HNNLO are compared with an NLO calculation and the POWHEG and MC@NLO implementations780

in SHERPA, where the parton shower has been stopped after the first emission. For the Higgs boson781

transverse momentum we find that the HNNLO result is significantly softer than both the POWHEGand782

the MC@NLO (α=1) sample - both have a significant shape distortion w.r.t. HNNLO over the fullp⊥(H)783

range. In contrast the NLO and the MC@NLO (α=0.03) result have a similar shape as HNNLO in the784

mid-p⊥ region, before developing a harder tail. The shape differences in the low-p⊥ region, essentially785

below p⊥(H) of about20 GeV, can be attributed to resummation effects. The picture becomes even786

more interesting when considering jet rates at the matrix element level. Here, both the POWHEG and787

the MC@NLO (α=1) sample have more 1 than 0-jet events, clearly at odds with thethree other samples.788

Of course, switching on the parton shower will lead to a migration to higher jet bins, as discussed in789

the next paragraph. With this in mind, one could argue that the 1-jet rates in both the POWHEG and790

the MC@NLO (α=1) sample seem to be in fair agreement with theinclusive1-jet rate of HNNLO- this791

however does not resolve the difference in the 0-jet bin, andultimately it nicely explains why these two792

samples produce a much harder radiation tail than HNNLO.793

In Fig. 22 now all plots are at the shower level. We can summarise the findings of this figure794

as follows: In the SHERPA implementation, the POWHEG and MC@NLO (α=1) results exhibit fairly795

November 18, 2011 – 11 : 26 DRAFT 52

HNNLO

Sherpa NLO

Sherpa POWHEG



10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.60.8

11.21.41.61.8

2

pT(H) [GeV]

Ratiowrt.HNNLO

HNNLO

Sherpa NLO

Sherpa POWHEG


Sherpa MC@NLO α = 0.0310−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 1000

0.20.40.60.8

11.21.4

pT(H) [GeV]Ratiowrt.HNNLO

HNNLO

Sherpa NLO

Sherpa POWHEG


Sherpa MC@NLO α = 0.0310−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 1000

0.20.40.60.8

11.21.4

pT(H) [GeV]

Ratiowrt.HNNLO

HNNLO

Sherpa POWHEG



10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 1000

0.20.40.60.8

11.21.4

pT(H) [GeV]

Ratiowrt.HNNLO

HNNLO

Sherpa NLO

Sherpa POWHEG



10−1

1

dσ/dm

ll[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

mll [GeV]

Ratio

HNNLO

Sherpa NLO

Sherpa POWHEG



5

10

15

20

25

30

35

σ(N

jet)[fb]

0 1 20

0.20.40.60.8

11.21.4

NjetRatiowrt.HNNLO

Fig. 22: The Higgs transverse momentum in all events, in events with 0, 1, and 2 and more jets, the invariant leptonmass, and the jet multiplicities inpp→ h→ e−µ+νeνµ production. Here different approaches are compared witheach other: two fixed order parton-level calculations at NNLO (HNNLO, black solid) and NLO (black, dashed),and three matched results in the SHERPA implementations (POWHEG, blue and MC@NLO with α = 1, reddashed and withα = 0.03, red solid). The yellow uncertainty band is given by the scale uncertainties of HNNLO.

identical trends for most observables, in particular, the Higgs boson transverse momentum in various796

samples tends to be harder than the pure NLO result, HNNLO, or MC@NLO (α=0.03). Comparing797

HNNLO with the NLO result and MC@NLO (α=0.03) we find that in most cases the latter two agree798

fairly well with each other, while there are differences with respect to HNNLO. In the low-p⊥ region of799

the Higgs boson, the difference seems to be well described bya globalK-factor of about 1.3-1.5, while800

HNNLO becomes softer in the high-p⊥ tail, leading to a sizable shape difference. One may suspectthat801

this is due to a different description of configurations withtwo jets, where quantum interferences lead to802

non-trivial correlations of the outgoing particles in phase space, which, of course, are correctly accounted803

for in HNNLO, while the other results either do not include such configurations (the parton-level NLO804

curve) or rely on the spin-averaged and therefore correlation-blind parton shower to describe them. This805

is also in agreement with findings in the jet multiplicities,where the MC@NLO (α=0.03) and the NLO806

result agree with HNNLO in the 0-jet bin, while the POWHEGand MC@NLO (α=1) result undershoot by807

about 30%, reflecting their larger QCD activity. For the 1- and 2-jet bins, however, their agreement with808

the HNNLO result improves and in fact, as already anticipated from theME-level results, multiplying809

the POWHEG result with a globalK-factor of about 1.5 would bring it to a very good agreement with810

HNNLO for this observable. In contrast the MC@NLO (α=0.03) result undershoots HNNLO in the 1-jet811

bin by about 25% and in the 2-jet bin by about a factor of 4. Clearly here support from higher order812

tree-level matrix elements like in ME+PS or MENLOPS-type [121,122] approaches would be helpful.813

Where not stated otherwise, in the following sections, all curves relate to an NLO matching ac-814

cording to the MC@NLO prescription withα = 0.03.815

November 18, 2011 – 11 : 26 DRAFT 53

4.3.3 Perturbative uncertainties816

The impact of scale variations on the Higgs transverse momentum in all events and in events with 0,817

1 and 2 or more jets is exhibited in Fig. 23, where a typical variation by factors of 2 and 1/2 has been818

performed around the default scalesµR = µF = mH . For the comparison with the fixed scale we find819

that distributions that essentially are of leading order accuracy, such asp⊥ distributions of the Higgs820

boson in the 1-jet region or the 1-jet cross section, the scale uncertainty is of the order of 40%, while821

for results in the resummation region of the parton shower, i.e. the 0-jet cross section or the Higgs boson822

transverse momentum in the 0-jet bin, the uncertainties aresmaller, at about 20%.823

In contrast differences between the functional form of the scales choice are smaller, as exemplified824

in Fig. 24, where the central valueµF = µR = mH/2 has been compared with an alternative scale825

µF = µR = mT,H/2 =√m2

H + p2⊥,H/2. It should be noted, though that there the two powers ofαS826

related to the effectiveggH vertex squared have been evaluated at a scalemH . Anyway, with this in827

mind it is not surprising that differences only start to become sizable in the largep⊥ regions of additional828

radiation, where they reach up to about 40%.829

TODO: Scale factor variation plots are currently at parton level, i.e after first emission. Update830

with or add shower level plots.831

Rather than performing a full PDF variation according to therecipe in [123], in Fig. 25 results for832

MSTW08 NLO, have been compared to those obtained with the central NLO set of CT10. By far and833

large, there is no sizable difference in any relevant shape.However, a difference of about 10% can be834

observed in the total normalisation, which can be traced back to the combined effect of minor differences835

in both the gluon PDF and the value ofαS.836

4.3.4 Parton to hadron level837

In Fig. 26 the impact of adding parton showering, fragmentation and the underlying event is exemplified838

for the same observables as in the figures before. In addition, the invariant lepton mass and the jet839

multiplicities are exhibited at the same stages of event generation. All curves are obtained by an NLO840

matching according to the MC@NLO prescription withα = 0.03. In the following, the CT10 PDF was841

used to be able to use the corresponding tuning of the non-perturbative SHERPAparameters.842

In general, the effect of parton showering is notable, resulting in a shift of the transverse momen-843

tum of the Higgs boson away from very low transverse momenta to values of about20 − 80 GeV with844

deviations up to 10%. This effect is greatly amplified in the exclusive jet multiplicities, where theexclu-845

sive1-jet bin on the parton level feeds down to higher jet multiplicities emerging in showering, leading846

to a reduction of about 50% in that bin (which are of course compensated by higher bins such that the847

net effect on theinclusive1-jet bin is much smaller). A similar effect can be seen in theHiggs transverse848

momentum in the exclusive 0-jet bin, where additional radiation allows for larger transverse kicks” of849

the Higgs boson without actually resulting in jets. In all cases, however, the additional impact of the850

underlying event is much smaller, with a maximal effect of about 15-20% in the 2-jet multiplicity and in851

some regions of the Higgs transverse momentum.852

4.3.5 Non-perturbative uncertainties853

In the following, uncertainties due to non-perturbative effects have been estimated. Broadly speak-854

ing, two different physics reasons have been investigated,namely the impact of fragmentation, which855

has been assessed by switching from SHERPA’s default cluster fragmentation [124] to the Lund string856

fragmentation [125] encoded in PYTHIA 6.4 [126] and suitably interfaced10, and the impact of varia-857

tions in the modelling of the underlying event. There SHERPA’s model, which is based on [127], has858

10Both fragmentation schemes in the SHERPA framework have been tuned to the same LEP data, yielding a fairly similarquality in the description of data.

November 18, 2011 – 11 : 26 DRAFT 54

µ = mh

µ = 12 . . . 2mh

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

µ = mh

µ = 12 . . . 2mh

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

pT(H), 0-jet [GeV]

Ratio

µ = mh

µ = 12 . . . 2mh

10−3

10−2

10−1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 1-jet [GeV]

Ratio

µ = mh

µ = 12 . . . 2mh

0

5

10

15

20

25

30

35

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 23: The impact of scale variation by a factor of 2 and 1/2 on the transverse momentum of the Higgs boson inall events, events with no and with one jet, and on jet multiplicities. All curves are obtained by an NLO matchingaccording to the MC@NLO prescription withα = 0.03.

been modified such that the transverse activity (the plateauregion ofNch in the transverse region) is859

increased/decreased by 10%.860

We find that in all relevant observables the variation of the fragmentation model leads to differ-861

ences which are consistent with statistical fluctuations inthe different Monte Carlo samples. This is862

illustrated by the Higgs boson transverse momentum and the jet multiplicities, displayed in Fig. 27.863

Similarly, differences due to the underlying event on the Higgs boson transverse momentum and864

various jet-related observables are fairly moderate and typically below 10%. This is especially true for jet865

multiplicities, where the 10% variation of the underlying event activity translates into differences of the866

order of 2-3% only. However, it should be stressed here that the variation performed did not necessarily867

affect the hardness of the parton multiple scatterings, i.e. the amount of jet production in secondary868

parton scatters, but rather increased the number of comparably soft scatters, leading to an increased soft869

activity. In order to obtain a more meaningful handle on jet production due to multiple parton scattering870

dedicated analyses are mandatory in order to validate and improve the relatively naive model employed871

here.872

November 18, 2011 – 11 : 26 DRAFT 55

µ0 =12 m

h⊥

µ0 =12 mh

10−4

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

µ0 =12 m

h⊥

µ0 =12 mh

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

pT(H), 0-jet [GeV]

Ratio

µ0 =12 m

h⊥

µ0 =12 mh

10−4

10−3

10−2

10−1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 1-jet [GeV]

Ratio

µ0 =12 m

h⊥

µ0 =12 mh

0

5

10

15

20

25

30

35

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 24: Differences in the transverse momentum of the Higgs boson inall events, in events with no and with onejet, and on jet multiplicities due to varying the functionalform of the renormalisation and factorisation scales fromµF,R = mH to µF,R = mT,H . The yellow uncertainty band relates to the statistical fluctuations in the referencehistogram. All curves are obtained by an NLO matching according to the MC@NLO prescription withα = 0.03.

November 18, 2011 – 11 : 26 DRAFT 56

MSTW08

CT10

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

MSTW08

CT10

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

pT(H), 0-jet [GeV]

Ratio

MSTW08

CT10

10−3

10−2

10−1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 1-jet [GeV]

Ratio

MSTW08

CT10

0

5

10

15

20

25

30

35

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 25: The impact of different choices of PDFs - MSTW08 NLO (black) and CT10 NLO (red) - for amH =

160 GeV on the transverse momentum of the Higgs boson in all events, events with no and with one jet, and onjet multiplicities. The yellow uncertainty band relates tothe statistical fluctuations in the reference histogram. Allcurves are obtained by an NLO matching according to the MC@NLO prescription withα = 0.03.

November 18, 2011 – 11 : 26 DRAFT 57

Hadron Level w/ MPI

Hadron Level w/o MPI

Shower Level

Parton Level

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

Hadron Level w/ MPI


Shower Level

Parton Level

10−4

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

pT(H), 0-jet [GeV]Ratio

Hadron Level w/ MPI


Shower Level

Parton Level

10−3

10−2

10−1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 1-jet [GeV]

Ratio

Hadron Level w/ MPI


Shower Level

Parton Level

10−4

10−3

10−2

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 2-jet [GeV]

Ratio

Hadron Level w/ MPI


Shower Level

Parton Level

10−1

1

dσ/dm

ll[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

mll [GeV]

Ratio

Hadron Level w/ MPI


Shower Level

Parton Level

0

5

10

15

20

25

30

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 26: The impact of going from the parton level (orange) over the parton shower level (red) to the hadron levelwithout (blue) and with (black) the underlying event. The error band relates to the variation of the reference result- the full simulation - due to scale effects in the matrix element. All curves are obtained by an NLO matchingaccording to the MC@NLO prescription withα = 0.03.

fragmentation uncertainty

Cluster

Lund

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

fragmentation uncertainty

Cluster

Lund

0

5

10

15

20

25

30

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 27: The impact of different fragmentation models - cluster (black) and string (red) - for amH = 160 GeV onthe transverse momentum of the Higgs boson in all events, andon jet multiplicities. All curves are obtained by anNLO matching according to the MC@NLO prescription withα = 0.03.

November 18, 2011 – 11 : 26 DRAFT 58

MPI variation

MPI up

MPI central

MPI down

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H) [GeV]

Ratio

MPI variation

MPI up

MPI central

MPI down

10−4

10−3

10−2

10−1

1

dσ/dpT(H

)[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

pT(H), 0-jet [GeV]

Ratio

MPI variation

MPI up

MPI central

MPI down

10−3

10−2

10−1

dσ/dpT(H

)[fb/GeV

]

0 100 200 300 400 500

0.6

0.8

1

1.2

1.4

pT(H), 1-jet [GeV]

Ratio

MPI variation

MPI up

MPI central

MPI down

0

5

10

15

20

25

30

σ(N

jet)[fb]

0 1 2

0.6

0.8

1

1.2

1.4

Njet

Ratio

Fig. 28: Differences in the Higgs boson transverse momentum in all events, in events with 0, 1, and in jet multiplic-ities due to variations in the modelling of the underlying event - central (black) vs. increased (blue) and suppressed(red) activity - for amH = 160 GeV. All curves are obtained by an NLO matching according to the MC@NLO

prescription withα = 0.03.

November 18, 2011 – 11 : 26 DRAFT 59

5 The Gluon-Fusion Process11873

In the first volume of this Handbook, the status of the inclusive cross section for Higgs production in874

gluon fusion was summarized [6]. Corrections arising from higher-order QCD, electroweak effects, as875

well as contributions beyond the commonly-used effective theory approximation were analyzed. Un-876

certainties arising from missing terms in the perturbativeexpansion, as well as imprecise knowledge877

of parton distribution functions, were estimated to range from approximately 15-20%, with the precise878

value depending on the Higgs boson mass.879

Our goal in this second volume is to extend the previous studyof the gluon-fusion Higgs mecha-880

nism to include differential cross sections. The motivation for such investigations is clear; experimental881

analyses must impose cuts on the final state in order to extract the signal from background. A precise882

determination of the corresponding signal acceptance is needed. Hopefully, it is computed to the same883

order in the perturbative expansion as the inclusive cross section. Possible large logarithms that can884

occur when cuts are imposed should be identified and controlled. In the case of gluon-fusion Higgs885

production, numerous tools exist to perform a precise theoretical calculation of the acceptance. The886

fully differential Higgs cross section to next-to-next-to-leading order (NNLO) in QCD is available in887

two parton-level Monte-Carlo simulation codes, FEHiP [128, 129] and HNNLO [109, 130]. The Higgs888

transverse momentum spectrum has been studied at the next-to-leading (NLO) order level, and supple-889

mented with next-to-next-to leading logarithmic (NNLL) resummation of smallpT logarithms, by several890

groups [131–133]. Other calculations and programs for studying Higgs production in the gluon-fusion891

channel are available, as discussed throughout this Section. All of these results are actively used by the892

experimental community.893

We aim in this Section to discuss several issues that arise when studying differential results in the894

gluon-fusion channel which are relevant to LHC phenomenology. A short summary of the contents of895

this report are presented below.896

– The amplitude for gluon-fusion production of the Higgs begins at one loop. An exact NNLO cal-897

culation of the cross section would therefore require a multi-scale, three-loop calculation. Instead,898

an effective field theory approach is utilized, which is valid for relatively light Higgs masses. The899

validity of this effective-theory approach has been extensively studied for the inclusive cross sec-900

tion, and was reviewed in the first volume of this Handbook [6]. However, the accuracy of the901

effective-theory approach must also be established for differential distributions. For example, fi-902

nite top-mass corrections of order(pHT /mt)2 can appear beyond the effective theory. It is also903

clear that bottom-quark mass effects on Higgs differentialdistributions cannot be accurately mod-904

eled within the effective theory. These issues are investigated in Section 5.1 of this report. It is905

demonstrated thatO(10%) distortions of the Higgs transverse momentum spectrum are possible906

in the high-pT region.907

– The composition of the background to Higgs production in gluon fusion, followed by the decay908

H → W+W−, differs dramatically depending on how many jets are observed together with the909

Higgs in the final state. In the zero-jet bin, the dominant background comes from continuum910

production ofW+W−. In the 1- and 2-jet bins, top-quark pair production becomeslarge. The911

optimization of the experimental analysis therefore utilizes a split into different jet-multiplicity912

bins. Such a split induces large logarithms associated withthe ratio of the Higgs mass over the913

definingpT of the jet. The most natural method of evaluating the theoretical uncertainty in the zero-914

jet bin [134] leads to a smaller estimated uncertainty than the error on the inclusive cross section.915

This indicates a possible cancellation between logarithmsof thepT cut and the large corrections916

to the Higgs cross section, and a potential underestimate ofthe theoretical error. An improved917

prescription for estimating the perturbative uncertaintyin the exclusive jet bins is discussed in918

11M. Grazzini, F. Petriello, J. Qian, F. Stoeckli (eds.); E.A.Bagnaschi, A. Banfi, D. de Florian, G. Degrassi, G. Ferrera,G. Salam, P. Slavich, I. Stewart, F. Tackmann, D. Tommasini,A. Vicini, W. Waalewijn, G. Zanderighi

November 18, 2011 – 11 : 26 DRAFT 60

Section 5.2. Evidence is given that the cancellation suggested above does indeed occur, and that919

the uncertainty in the zero-jet bin is in fact nearly twice aslarge as the estimated error of the920

inclusive cross section. Further evidence for the accidental cancellation between large Sudakov921

logarithms and corrections to the total cross section is given in Section 5.3, where it is shown that922

different prescriptions for treating the uncontrolledO(α3s) corrections to the zero-jet event fraction923

lead to widely varying predictions at the LHC.924

– A significant hinderance in our modeling of the cross section in exclusive jet bins is our inability925

to directly resum the large logarithms mentioned above. Instead, we must obtain insight into the926

all-orders structure of the jet-vetoed cross section usingrelated observables. An example of such927

a quantity is the Higgs transverse momentum spectrum. ThroughO(αs) it is identical to the jet-928

vetoed cross section, since at this order the Higgs can only recoil against a single parton whose929

pT matches the Higgs. The large logarithms which arise when theHiggs transverse momentum930

becomes small can be resumed. Section 5.4 presents un updated version of the codeHqT, which931

matches the NNLL resumption of the Higgs transverse momentum with the exact NLOpT spec-932

trum obtained from fixed order. Another such variable used togain insight into the effect of a933

jet veto is beam thrust, which is equivalent to a rapidity-weighted version of the standard variable934

HT . The resummation of beam thrust, and the reweighing of the Monte Carlo program MC@NLO935

to the next-to-next-to-leading logarithmic prediction for beam thrust in order to gain insight into936

how well the jet-vetoed cross section is predicted by currently used programs, is described in937

Section 5.5.938

Unlike the first volume of this report, no explicit numbers are given for use in experimental studies. The939

possible distributions of interest in the myriad studies performed at the LHC are too diverse to compile940

here. Our goal is to identify and discuss the relevant issuesthat arise, and to give prescriptions for their941

solution. We must also stress that such prescriptions are not set in stone, and are subject to change if942

theoretical advances occur. For example, if an exact NNLO calculation of the Higgs cross section with943

the full dependence on the quark masses becomes available, or the jet-vetoed Higgs cross section is944

directly resumed, these new results must be incorporated into the relevant experimental investigations.945

5.1 Finite quark mass effects in the SM gluon fusion process in POWHEG946

E.A. Bagnaschi, G. Degrassi, P. Slavich, A. Vicini947

5.1.1 Introduction948

An accurate description of Higgs boson production via gluonfusion, not only of the total cross section949

but also of all the differential distributions, will be paramount to study in detail the nature and properties950

of the Higgs boson – should the latter be detected at the LHC – or to set stringent exclusion limits on951

its mass. The description of the process in the complete theory can be approximated, in many cases, by952

an effective theory (ET) obtained by taking the limit of infinite mass for the top quark running in the953

lowest-order loop that couples the Higgs to the gluons, and neglecting all the other quark flavors. This954

limit greatly simplifies many calculations, reducing the number of loops that have to be considered by955

one. On the other hand it is important, when possible, to check whether the effect of an exact treatment956

of the quark contributions is significant compared to the actual size of the theoretical uncertainty.957

The validity of the ET approach has been carefully analyzed for the total cross section. The latter958

receives very large next-to-leading order (NLO) QCD corrections, which have been computed first in959

the ET [62, 135] and then retaining the exact dependence on the masses of the quarks that run in the960

loops [63, 136–139]. The NLO results computed in the ET and then rescaled by the exact leading-order961

(LO) result with full dependence on the top and bottom quark masses provide a description accurate at962

the few per cent level forMH ≤ 2mt. The deviation for2mt ≤ MH ≤ 1 TeV does not exceed the963

10% level. The next-to-next-to-leading order (NNLO) QCD corrections to the total cross section are still964

November 18, 2011 – 11 : 26 DRAFT 61

large, and have been computed in the ET [140–142]. The finite top mass effects at NNLO QCD have965

been studied in Refs. [143–146] and found to be small. The resummation to all orders of soft gluon966

radiation has been studied in Ref. [147], only in the ET. The leading third-order (NNNLO) QCD terms967

have been discussed in the same approximation [148]. The role of electroweak (EW) corrections has been968

discussed in Refs. [21,23–26,149,150] and found to be, for alight Higgs, of the same order of magnitude969

as the QCD theoretical uncertainty. The impact of mixed QCD-EW corrections has been discussed970

in Ref. [151]. The residual uncertainty on the total cross section depends mainly on the uncomputed971

higher-order QCD effects and on the uncertainties that affect the parton distribution functions of the972

proton [6,99,123].973

The Higgs differential distributions have first been studied at NLO QCD in Refs. [152, 153] and974

at NNLO QCD, in the ET, in Refs. [128, 129]. The NLO-QCD results including the exact dependence975

on the top and bottom quark masses were first included in the code HIGLU based on Ref. [63]. More976

recently, the same calculation was repeated in Refs. [154–156]. The latter discussed at NLO-QCD the977

role of the bottom quark, for light Higgs boson masses. An accurate description of the Higgs differ-978

ential distributions, in the ET, including NLO-QCD resultsmatched at NNLL QCD with the transverse979

momentum resummation, has been provided in Refs. [131, 132]and implemented in the codeResbos.980

The Higgs transverse momentum distribution, in the ET, including NNLO-QCD results and matched at981

NNLL QCD with the resummation of soft-gluon emissions, has been presented in Ref. [133] and is im-982

plemented in the codeHqT. The latter allows for a quite accurate estimate of the perturbative uncertainty983

on this distribution, which turns out to be of the order of±10% for light Higgs and for Higgs transverse984

momentumpHT ≤ 100 GeV [157].985

The shower Montecarlo (SMC) codes matching NLO-QCD resultswith QCD Parton Shower (PS)986

[104, 113] consider the gluon fusion process only in the ET. Recently, a step toward the inclusion of the987

finite quark mass effects in PS was taken in Ref. [158], where parton-level events for Higgs production988

accompanied by zero, one or two jets are generated with matrix elements obtained in the ET and then,989

before being passed to the PS, they are re-weighted by the ratio of the full one-loop amplitudes over the990

ET ones.991

In Ref. [108] the implementation in thePOWHEG framework [111,112,159] of the NLO-QCD ma-992

trix elements for the gluon fusion, including the exact dependence on the top and bottom quark masses,993

has been presented. We discuss here the effect of the exact treatment of the quark masses on the Higgs994

transverse momentum distribution, comparing the results of the oldPOWHEG release, obtained in the ET,995

with those of this new implementation [108]. In particular,we consider here the matching ofPOWHEG996

with thePYTHIA [126] PS.997

5.1.2 Quark mass effects in thePOWHEG framework998

In this section we briefly discuss the implementation of the gluon-fusion Higgs production process in999

thePOWHEG BOX framework, following closely Ref. [104]. We fix the notationkeeping the discussion at1000

a general level, and refer to Ref. [108] for a detailed description and for the explicit expressions of the1001

matrix elements. The generation of the hardest emission is done inPOWHEG according to the following1002

formula:1003

dσ = B(Φ1) dΦ1

{∆(Φ1, p

minT

)+∆

(Φ1, pT

) R(Φ1,Φrad

)

B(Φ1

) dΦrad

}

+∑

q

Rqq

(Φ1,Φrad

)dΦ1dΦrad . (15)

In the equation above the variablesΦ1 ≡ (M2, Y ) denote the invariant mass squared and the rapidity of1004

the Higgs boson, which describe the kinematics of the Born (i.e., lowest-order) processgg → φ. The1005

variablesΦrad describe the kinematics of the additional final-state parton in the real emission processes.1006

November 18, 2011 – 11 : 26 DRAFT 62

[GeV]HT

p

0 50 100 150 200 250 300

R

0.85

0.9

0.95

1

1.05

1.1

1.15

LH

C H

IGG

S X

S W

G 2

011

LHC 7 TeV NLO-QCDratio of normalized distributionsR=(exact top+bottom)/(effective theory)

=125 GeVHm

=165 GeVHm

=500 GeVHm

[GeV]HT

p

0 50 100 150 200 250 300

R

0.85

0.9

0.95

1

1.05

1.1

1.15

LH

C H

IGG

S X

S W

G 2

011

LHC 7 TeV POWHEG+PYTHIAratio of normalized distributionsR=(exact top+bottom)/(effective theory)

=125 GeVHm

=165 GeVHm

=500 GeVHm

Fig. 29: Ratio, for different values of the SM Higgs boson mass, of thenormalized Higgs transverse momentumdistribution computed with exact top and bottom mass dependence over the one obtained in the ET. Left: ratio ofthe NLO-QCD predictions. Right: ratio of thePOWHEG+PYTHIA predictions.

The factorB(Φ1) in Eq. (15) is related to the total cross section computed at NLO in QCD. It contains1007

the value of the differential cross section, including realand virtual radiative corrections, for a given1008

configuration of the Born final state variables, integrated over the radiation variables. The integral of1009

this quantity ondΦ1, without acceptance cuts, yields the total cross section and is responsible for the1010

correct NLO-QCD normalization of the result. The terms within curly brackets in Eq. (15) describe the1011

real emission spectrum of an extra parton: the first term is the probability of not emitting any parton with1012

transverse momentum larger than a cutoffpminT , while the second term is the probability of not emitting1013

any parton with transverse momentum larger than a given value pT times the probability of emitting a1014

parton with transverse momentum equal topT . The sum of the two terms fully describes the probability1015

of having either zero or one additional parton in the final state. The probability of non-emission of a1016

parton with transverse momentumkT larger thanpT is obtained using thePOWHEG Sudakov form factor1017

∆(Φ1, pT ) = exp

{−∫dΦrad

R(Φ1,Φrad)

B(Φ1)θ(kT − pT )

}, (16)

where the Born squared matrix element is indicated byB(Φ1) and the squared matrix element for the real1018

emission of an additional parton can be written, considering the subprocessesgg → φg andgq → φq, as1019

R(Φ1,Φrad) = Rgg(Φ1,Φrad) +∑

q

[Rgq(Φ1,Φrad) +Rqg(Φ1,Φrad)

]. (17)

Finally, the last term in Eq. (15) describes the effect of theqq → φg channel, which has been kept apart1020

in the generation of the first hard emission because it does not factorize into the Born cross section times1021

an emission factor.1022

The NLO-QCD matrix elements used in this implementation have been computed in Refs. [138,1023

139]. We compared the numerical results for the distributions with those of the codeFehiPro [136],1024

finding good agreement. We also checked that, in the case of a light Higgs and considering only the top1025

contribution, the ET provides a very good approximation of the exact result for small values of the Higgs1026

transverse momentumpHT , and only whenpHT ≥ mt does a significant discrepancy appear, due to the1027

fact that the internal structure of the top-quark loop is resolved.1028

November 18, 2011 – 11 : 26 DRAFT 63

In order to appreciate the importance of the exact treatmentof the quark masses, we compare1029

in Fig. 29 the normalized distributions computed with the exact top and bottom mass dependence with1030

the corresponding distributions obtained in the ET. The normalized distributions are defined dividing1031

each distribution by the corresponding total cross section, and allow a comparison of the shape of the1032

distributions. In the left panel of Fig. 29 we plot the ratio of the normalizedpHT distributions (exact1033

over ET) computed using the real radiation matrix elements that enter in the NLO-QCD calculation, for1034

different values of the Higgs mass (MH = 125, 165, 500 GeV). The plot shows that, for a light Higgs,1035

the bottom-quark contribution induces positiveO(10%) corrections in the intermediatepHT range. On1036

the other hand, for a heavy Higgs, the bottom quark contribution is negligible, while the exact treatment1037

of the top-quark contribution tends to enhance the distribution at smallpHT and significantly reduce it at1038

largepHT (where in any case the cross section is small).1039

The matching of the NLO-QCD results with a QCD PS is obtained by using the basicPOWHEG1040

formula, Eq. (15), for the first hard emission, and then by vetoing in the PS any emission with a virtuality1041

larger than the one of the first emission. The use of the exact matrix elements in Eq. (15), and in1042

particular in thePOWHEG Sudakov form factor, Eq. (16), has an important impact on thepHT distribution1043

when compared with the distribution obtained in the ET. Indeed, one should observe that thePOWHEG1044

Sudakov form factor is a process-dependent quantity. For a given transverse momentumpT , in the1045

exponent we find the integral of the ratio of the full squared matrix elementsR/B over all the transverse1046

momentakT larger thanpT .1047

The results of the matching ofPOWHEG with the PYTHIA PS are illustrated in the right plot of1048

Fig. 29, where we show the ratio of the normalizedpHT distribution computed with exact top and bottom1049

mass dependence over the corresponding distribution computed in the ET, for the same values ofMH as1050

in the left plot. We shall first discuss the case of a light Higgs boson, withMH = 125 GeV. For smallpHT ,1051

the Sudakov form factor with exact top and bottom quark mass dependence∆(t+b, exact) is smaller than1052

the corresponding factor∆(t,∞) with only top in the ET, because we have thatR(t+ b, exact)/B(t +1053

b, exact) > R(t,∞)/B(t,∞). The inequality holds for two reasons:i) thepHT distribution is propor-1054

tional to the squared real matrix elementR and, forpHT < 200 GeV,R(t + b, exact) > R(t,∞), as1055

has been discussed in Refs. [108, 154, 156];ii) the bottom quark reduces the LO cross section, with1056

respect to the case with only the top quark in the ET [63]. Thus, for smallpHT the Sudakov form factor1057

suppresses thepHT distribution by almost 10% with respect to the results obtained in the ET. Since the1058

emission probability is also proportional to the ratioR/B, as can be read from Eq. (15), starting from1059

pHT ≃ 30 GeV this factor prevails over the Sudakov factor, and the distribution with exact dependence on1060

the quark masses becomes larger than the one in the ET by slightly more than 10% – as already observed1061

at NLO QCD in the left plot. We remark that the effects due to the exact treatment of the masses of1062

the top and bottom quarksi) are of the same order of magnitude as the QCD perturbative theoretical1063

uncertainty estimated withHqT andii) have a non-trivial shape for different values ofpHT . If added to1064

theHqT prediction, these effects would modify in a non-trivial waythe prediction of the central value of1065

the distribution.1066

A different behaviour is found in the case of a heavy Higgs boson, withMH = 500 GeV, because1067

the bottom quark plays a negligible role. At NLO QCD only the top quark mass effects are relevant,1068

at largepHT , yielding a negative correction. In turn, the Sudakov form factor, evaluated for smallpHT ,1069

is larger than in the ET (in factR(t + b, exact)/B(t + b, exact) < R(t,∞)/B(t,∞)), yielding what1070

we would call a Sudakov enhancement. Also in this case, starting from pHT ≃ 70 GeV, the effect of the1071

emission probability factorR/B prevails over the effect of the Sudakov form factor, leadingto negative1072

corrections with respect to the ET case.1073

5.1.3 Summary1074

An improved release of the code for Higgs boson production ingluon fusion in thePOWHEG framework1075

has been prepared [108], including the complete NLO-QCD matrix elements with exact dependence on1076

November 18, 2011 – 11 : 26 DRAFT 64

the top and bottom quark masses. This code allows a full simulation of the process, matching the NLO1077

results with the SMCPYTHIA.1078

The quark-mass effects on the total cross section and on the Higgs rapidity distribution are at the1079

level of a few percent. On the other hand, the bottom quark contribution is especially relevant in the1080

study of the transverse momentum distribution of a light Higgs boson. Indeed, the bottom contribution1081

enhances the real emission amplitude with respect to the result obtained in the ET. The outcome is a non-1082

trivial distortion of the shape of the Higgs transverse momentum distribution, at the level ofO(10%) of1083

the result obtained in the ET. These effects are comparable to the present estimates of the perturbative1084

QCD theoretical uncertainty.1085

5.2 Perturbative uncertainties in exclusive jet bins1086

I. W. Stewart, F. J. Tackmann1087

5.2.1 Overview1088

In this Section we discuss the evaluation of perturbative theory uncertainties in predictions for exclusive1089

jet cross sections, which have a particular number of jets inthe final state. This is relevant for mea-1090

surements where the data are divided into exclusive jet bins, and is usually done when the background1091

composition strongly depends on the number of jets, or when the overall sensitivity can be increased by1092

optimizing the analysis for the individual jet bins. The primary example is theH → WW analysis,1093

which is performed separately in exclusive0-jet, 1-jet, and2-jet channels. Other examples are vector-1094

boson fusion analyses, which are typically performed in theexclusive2-jet channel, boostedH → bb1095

analyses that include a veto on additional jets, as well asH → ττ andH → γγ which benefit from1096

improved sensitivity when the Higgs recoils against a jet. When the measurements are performed in1097

exclusive jet bins, the perturbative uncertainties in the theoretical predictions must also be evaluated sep-1098

arately for each individual jet bin [134]. When combining channels with different jet multiplicities, the1099

correlations between the theoretical uncertainties can besignificant and must be taken into account [160].1100

We will use the notationσN for anexclusiveN -jet cross section (with exactlyN jets), and the notation1101

σ≥N for an inclusiveN -jet cross section (withN or more jets). Three possible methods for evaluating1102

the uncertainties in exclusive jet cross sections are1103

A) “Direct Exclusive Scale Variation”, utilized in Ref [134]. Here the uncertainties are evaluated by1104

directly varying the renormalization and factorization scales in the fixed-order predictions for each1105

exclusive jet cross sectionσN . The results are taken as 100% correlated, such that when adding1106

the exclusive jet cross sections one recovers the scale variation in the total cross section.1107

B) “Combined Inclusive Scale Variation”, as proposed in Ref. [160]. Here, the perturbative uncer-1108

tainties in the inclusiveN -jet cross sections,σ≥N , are treated as the primary uncertainties that1109

can be evaluated by scale variations in fixed-order perturbation theory. These uncertainties are1110

treated as uncorrelated for differentN . The exclusiveN -jet cross sections are obtained using1111

σN = σ≥N − σ≥N+1. The uncertainties and correlations follow from standard error propagation,1112

including the appropriate anticorrelations betweenσN andσN±1 related to the division into jet1113

bins.1114

C) “Uncertainties from Resummation with Reweighting.” Resummed calculations for exclusive jet1115

cross sections can provide uncertainty estimates that allow one to simultaneously include both1116

types of correlated and anticorrelated uncertainties as inmethods A and B. The magnitude of the1117

uncertainties may also be reduced from the resummation of large logarithms.1118

Method B avoids a potential underestimate of the uncertainties in individual jet bins due to strong can-1119

cellations that can potentially take place in method A. An explicit demonstration that different treatments1120

of the uncontrolled higher-orderO(α3s) terms in Method A can lead to very different LHC predictions1121

November 18, 2011 – 11 : 26 DRAFT 65

is given in Section 5.3. Method B produces realistic perturbative uncertainties for exclusive jet cross1122

sections when using fixed-order predictions for various processes. It is the main topic of this section,1123

which follows Ref. [160]. In Method C one can utilize higher-order resummed predictions for the exclu-1124

sive jet cross sections, which allow one to obtain improved central values and further refined uncertainty1125

estimates. This is discussed in the next section. The uncertainties from method B are more consistent1126

with the information one gains about jet-binning effects from using resummation.1127

For method B the theoretical motivation from the basic structure of the perturbative series is out-1128

lined in Sec. 5.2.2. An implementation for the example of the0-jet and1-jet bins is given in Sec. 5.2.3.1129

If theory predictions are required for irreducible backgrounds in jet bins, then the same method can be1130

used to evaluate the perturbative uncertainties, for e.g. in the case ofH → WW , theqq → WW and1131

gg → WW direct production channels.1132

Note that here we are only discussing the theoretical uncertainties due to unknown higher-order1133

perturbative corrections, which are commonly estimated using scale variation. Parametric uncertainties,1134

such as PDF andαs uncertainties, must be treated appropriately as common sources for all investigated1135

channels.1136

5.2.2 Theoretical Motivation1137

To start, we consider the simplest example of dividing the total cross section,σtotal, into anexclusive0-jet bin,σ0(pcut), and the remaininginclusive(≥ 1)-jet bin,σ≥1(p

cut),

σtotal =

∫ pcut

0dpdσ

dp+

∫

pcutdpdσ

dp≡ σ0(p

cut) + σ≥1(pcut) . (18)

Herep denotes the kinematic variable which is used to divide up thecross section into jet bins. A typical1138

example isp ≡ pjetT , defined by the largestpT of any jet in the event, such thatσ0(pcutT ) only contains1139

events with jets havingpT ≤ pcutT , andσ≥1(pcutT ) contains events with at least one jet withpT ≥ pcutT .1140

The definition ofσ0 may also include dependence on rapidity, such as only considering jets within the1141

rapidity range|ηjet| ≤ ηcut.1142

The phase space restriction definingσ0 changes its perturbative structure compared to that of1143

σtotal, and in general gives rise to an additional perturbative uncertainty which we denote by∆cut. This1144

can be thought of as an uncertainty related to large logarithms of pcut, or more generally as an uncer-1145

tainty associated to computing a less inclusive cross section, which is theoretically more challenging.1146

In Eq. (18) bothσ0 andσ≥1 depend on the phase space cut,pcut, and by construction this dependence1147

cancels inσ0 + σ≥1. Hence, the additional uncertainty∆cut induced bypcut must be 100% anticorre-1148

lated betweenσ0(pcut) andσ≥1(pcut), such that it cancels in their sum. For example, using a covariance1149

matrix to model the uncertainties and correlations, the contribution of∆cut to the covariance matrix for1150

{σ0, σ≥1} must be of the form1151

Ccut =

(∆2

cut −∆2cut

−∆2cut ∆2

cut

). (19)

The questions then are: (1) How can we estimate∆cut in a simple way, and (2) how is the perturbative1152

uncertainty∆total of σtotal related to the uncertainties ofσ0 andσ≥1? To answer these questions, we1153

discuss the perturbative structure of the cross sections inmore detail.1154

By restricting the cross section to the0-jet region, one restricts the collinear initial-state radiationfrom the colliding hard partons as well as the overall soft radiation in the event. This restriction on addi-tional emissions leads to the appearance of Sudakov double logarithms of the formL2 = ln2(pcut/Q) ateach order in perturbation theory, whereQ is the hard scale of the process. For Higgs production fromgluon fusion,Q =MH , and the leading double logarithms appearing atO(αs) are

σ0(pcutT ) = σB

(1− 3αs

π2 ln2

pcutT

MH+ · · ·

), (20)

November 18, 2011 – 11 : 26 DRAFT 66

whereσB is the Born (tree-level) cross section.1155

The total cross section only depends on the hard scaleQ, which means by choosing the scale1156

µ ≃ Q, the fixed-order expansion does not contain large logarithms and has the structure121157

σtotal ≃ σB[1 + αs + α2

s +O(α3s)]. (21)

As usual, varying the scale inαs (and the PDFs) one obtains an estimate of the size of the missing1158

higher-order terms in this series, corresponding to∆total.1159

The inclusive1-jet cross section has the perturbative structure

σ≥1(pcut) ≃ σB

[αs(L

2 + L+ 1) + α2s(L

4 + L3 + L2 + L+ 1) +O(α3sL

6)], (22)

where the logarithmsL = ln(pcut/Q). For pcut << Q these logarithms can get large enough to over-1160

come theαs suppression. In the limitαsL2 ≃ 1, the fixed-order perturbative expansion breaks down and1161

the logarithmic terms must be resummed to all orders inαs to obtain a meaningful result. For typical1162

experimental values ofpcut fixed-order perturbation theory can still be considered, but the logarithms1163

cause large corrections at each order and dominate the series. This means varying the scale inαs in1164

Eq. (22) tracks the size of the large logarithms and therefore allows one to get an estimate of the size of1165

missing higher-order terms caused bypcut, that corresponds to the uncertainty∆cut. Therefore, we can1166

approximate∆cut = ∆≥1, where∆≥1 is obtained from the scale variation forσ≥1.1167

The exclusive0-jet cross section is equal to the difference between Eqs. (21) and (22), and so hasthe schematic structure

σ0(pcut) = σtotal − σ≥1(p

cut)

≃ σB

{[1 + αs + α2

s +O(α3s)]−[αs(L

2+ L+ 1) + α2s(L

4+ L3+ L2+ L+ 1) +O(α3sL

6)]}.

(23)

In this difference, the large positive corrections inσtotal partly cancel against the large negative logarith-1168

mic corrections inσ≥1. For example, atO(αs) there is a value ofL for which theαs terms in Eq. (23)1169

cancel exactly. At thispcut the NLO 0-jet cross section has vanishing scale dependence and is equal1170

to the LO cross section,σ0(pcut) = σB . Due to this cancellation, a standard use of scale variationin1171

σ0(pcut) does not actually probe the size of the large logarithms, andthus is not suitable to estimate∆cut.1172

This issue impacts the uncertainties in the experimentallyrelevant region forpcut.1173

For example, forgg → H (with√s = 7TeV, MH = 165GeV, µf = µr = MH/2), one

finds [109,128–130]

σtotal = (3.32 pb)[1 + 9.5αs + 35α2

s +O(α3s)],

σ≥1

(pjetT ≥ 30GeV, |ηjet| ≤ 3.0

)= (3.32 pb)

[4.7αs + 26α2

s +O(α3s)]. (24)

In σtotal one can see the impact of the well-known largeK factors. (Using insteadµf = µr = MH1174

theαs andα2s coefficients inσtotal increase to11 and65.) In σ≥1, one can see the impact of the large1175

logarithms on the perturbative series. Taking their difference to getσ0, one observes a sizeable numerical1176

cancellation between the two series at each order inαs.1177

Since∆cut and∆total are by definition uncorrelated, by associating∆cut = ∆≥1 we are effec-1178

tively treating the perturbative series forσtotal andσ≥1 as independent with uncorrelated perturbative1179

uncertainties. That is, considering{σtotal, σ≥1}, the covariance matrix is diagonal,1180

(∆2

total 00 ∆2

≥1

), (25)

12These expressions for the perturbative series are schematic. The convolution with the parton distribution functions (PDFs)andµ dependent logarithms enter in the coefficients of the series, which are not displayed. (The single logarithms related tothePDF evolution are not the logarithms we are most interested in discussing.)

November 18, 2011 – 11 : 26 DRAFT 67

00

2

4

6

8

10

10 20 30 40 50 60 70 80 90 100

NLO

pcutT [GeV]

σ0(p

cut

T)

[pb]

NNLO

|ηjet|≤3.0

direct excl. scale variation

√s=7 TeV

MH =165 GeV

00

2

4

6

8

10

10 20 30 40 50 60 70 80 90 100

NLO

pcutT [GeV]

σ0(p

cut

T)

[pb]

NNLO

|ηjet|≤3.0

combined incl. scale variation

√s=7 TeV

MH =165 GeV

Fig. 30: Fixed-order perturbative uncertainties forgg → H +0 jets at NLO and NNLO. On the left, the uncertain-ties are obtained from the direct exclusive scale variationin σ0(pcutT ) betweenµ = MH/4 andµ = MH (methodA). On the right, the uncertainties are obtained by independently evaluating the inclusive scale uncertainties inσtotal andσ≥1(p

cut) and combining them in quadrature (method B). The plots are taken from Ref. [160].

00

1

10 20 30 40 50 60 70 80 90 100

0.2

0.4

0.6

0.8

NLO

pcutT [GeV]

f0(p

cut

T)

NNLO

|ηjet|≤3.0

direct excl. scale variation

√s=7 TeV

MH =165 GeV

00

1

10 20 30 40 50 60 70 80 90 100

0.2

0.4

0.6

0.8

NLO

pcutT [GeV]

f0(p

cut

T)

NNLO

|ηjet|≤3.0

combined incl. scale variation

√s=7 TeV

MH =165 GeV

Fig. 31: Same as Fig. 30 but for the0-jet fractionf0(pcutT ) = σ0(pcutT )/σtotal.

where∆total and∆≥1 are evaluated by separate scale variations in the fixed-order predictions forσtotal1181

andσ≥1. This is consistent, since for smallpcut the two series have very different structures. In particular,1182

there is no reason to believe that the same cancellations inσ0 will persist at every order in perturbation1183

theory at a givenpcut. It follows that the perturbative uncertainty inσ0 = σtotal − σ≥1 is given by1184

∆2total +∆2

≥1, and the resulting covariance matrix for{σ0, σ≥1} is1185

C =

(∆2

≥1 +∆2total −∆2

≥1

−∆2≥1 ∆2

≥1

). (26)

The∆≥1 contributions hare are equivalent to Eq. (19) with∆cut = ∆≥1. Note also that all of∆total1186

occurs in the uncertainty forσ0. This is reasonable from the point of view thatσ0 starts at the same order1187

in αs asσtotal and contains the same leading virtual corrections.1188

The limit ∆cut = ∆≥1 that Eq. (26) is based on is of course not exact. However, the preceding1189

arguments show that it is a more reasonable starting point than using a common scale variation for1190

the different jet bins as in method A, since the latter does not account for the additionalpcut induced1191

uncertainties. These two methods of evaluating the perturbative uncertainties are contrasted in Fig. 301192

for gg → H + 0 jets at NLO (light gray) and NNLO (dark gray) as a function ofpcutT (usingµ =MH/21193

for the central scale choice). The left panel shows the uncertainties from method A obtained from a direct1194

November 18, 2011 – 11 : 26 DRAFT 68

scale variation by a factor of two inσ0(pcutT ). For small values ofpcutT the cancellations that take place in1195

σ0(pcut) cause the error bands to shrink and eventually vanish atpcutT ≃ 25GeV, where there is an almost1196

exact cancellation between the two series in Eq. (23). In contrast, in the right panel the uncertainties1197

are obtained using the above method B by combining the independent inclusive uncertainties to obtain1198

the exclusive uncertainty,∆20 = ∆2

total + ∆2≥1. For large values ofpcutT this reproduces the direct1199

exclusive scale variation, sinceσ≥1(pcut) becomes small. On the other hand, for small values ofpcutT the1200

uncertainties estimated in this way are more realistic, because they explicitly estimate the uncertainties1201

due to the large logarithmic corrections. The features of this plot are quite generic. In particular, the1202

same pattern of uncertainties is observed for the Tevatron,when usingµ = MH as our central scale1203

(with µ = 2MH andµ = MH/2 for the range of scale variation), whether or not we only lookat1204

jets at central rapidities, or when considering the exclusive 1-jet cross section. We also note that using1205

independent variations forµf andµr does not change this picture, in particular theµf variation for1206

fixed µr is quite small. In Fig. 31 we again compare the two methods, but now for the event fraction1207

f0(pcutT ) = σ0(p

cutT )/σtotal. At large pcutT the curves asymptote to one and to zero uncertainty, and1208

both methods have smaller uncertainties forf0 than forσ0 alone. At smallpcutT the uncertainties inσ01209

are quite small with method A. In method B the uncertainties are more realistic, and there is now a1210

significant overlap between the bands at NLO and NNLO.1211

The generalization of the above discussion to more jets and several jet bins is straightforward. For1212

theN -jet bin we replaceσtotal → σ≥N , σ0 → σN , andσ≥1 → σ≥N+1, and take the appropriateσB. If1213

the perturbative series forσ≥N exhibits largeαs corrections due to its logarithmic series or otherwise,1214

then the presence of a different series of large logarithms inσ≥N+1 will again lead to cancellations when1215

we consider the differenceσN = σ≥N −σ≥N+1. Hence,∆≥N+1 will again give a better estimate for the1216

extra∆cut type uncertainty that arises from separatingσ≥N into σN andσ≥N+1. Plots for the one-jet1217

bin for Higgs production from gluon fusion can be found in Ref. [160].1218

5.2.3 Example Implementation forH + 0 Jet andH + 1 Jet Channels1219

To illustrate the implications for a concrete example we consider the0-jet and1-jet bins together with the1220

remaining(≥ 2)-jet bin. By construction only neighboring jet bins are correlated, so the generalization1221

to more jet bins is not any more complicated. We denote the total inclusive cross section byσtotal, and1222

the inclusive1-jet and2-jet cross sections byσ≥1 andσ≥2. Their respective absolute uncertainties are1223

∆total, ∆≥1, ∆≥2, and their relative uncertainties are given byδi = ∆i/σi. The exclusive0-jet cross1224

section,σ0, and1-jet cross section,σ1, satisfy the relations1225

σ0 = σtotal − σ≥1 , σ1 = σ≥1 − σ≥2 , σtotal = σ0 + σ1 + σ≥2 . (27)

Experimentally it is convenient to work with the exclusive0-jet and1-jet fractions defined as1226

f0 =σ0σtotal

, f1 =σ1σtotal

. (28)

Treating the inclusive uncertainties∆total, ∆≥1, ∆≥2 as uncorrelated, the covariance matrix for1227

the three quantities{σtotal, σ0, σ1} is given by1228

C =

∆2

total ∆2total 0

∆2total ∆2

total +∆2≥1 −∆2

≥1

0 −∆2≥1 ∆2

≥1 +∆2≥2

. (29)

The relative uncertainties and correlations forσ0 andσ1 directly follow from Eq. (29). Writing them interms of the relative quantitiesfi andδi, one gets

δ(σ0)2 =

1

f20δ2total +

( 1

f0− 1)2δ2≥1 ,

November 18, 2011 – 11 : 26 DRAFT 69

δ(σ1)2 =

(1− f0f1

)2δ2≥1 +

(1− f0f1

− 1)2δ2≥2 ,

ρ(σ0, σtotal) =

[1 +

δ2≥1

δ2total(1− f0)

2

]−1/2

,

ρ(σ1, σtotal) = 0 ,

ρ(σ0, σ1) = −[1 +

δ2totalδ2≥1

1

(1− f0)2

]−1/2[1 +

δ2≥2

δ2≥1

(1− f1

1− f0

)2]−1/2

. (30)

Alternatively, we can use{σtotal, f0, f1} as the three independent quantities. Their relative uncertaintiesand correlations following from Eq. (29) are then

δ(f0)2 =

( 1

f0− 1)2(

δ2total + δ2≥1

),

δ(f1)2 = δ2total +

(1− f0f1

)2δ2≥1 +

(1− f0f1

− 1)2δ2≥2 ,

ρ(f0, σtotal) =

[1 +

δ2≥1

δ2total

]−1/2

,

ρ(f1, σtotal) = − δtotalδ(f1)

,

ρ(f0, f1) = −(1 +

1− f0f1

δ2≥1

δ2total

)( 1

f0− 1) δ2totalδ(f0)δ(f1)

. (31)

The basic steps of the analysis are the same irrespective of the statistical model:1229

1. Independently evaluate the inclusive perturbative uncertaintiesδtotal, δ≥1, δ≥2 by appropriate scale1230

variations in the available fixed-order calculations.1231

2. Consider theδi uncorrelated and use Eqs. (27) or (28) to propagate them intothe uncertainties of1232

σ0,1 or f0,1.1233

For example, when using log-likelihoods, the independent uncertaintiesδtotal, δ≥1, δ≥2 are implemented1234

via three independent nuisance parameter.1235

In Step 1,δtotal can be taken from the NNLO perturbative uncertainty in the first Yellow Re-1236

port [6], whileδ≥1 is evaluated at relative NLO andδ≥2 at relative LO using any of HNNLO [109,130],1237

FEHiP [128, 129], or MCFM [161]. For the central scalesµf = µr = MH/2 should be used to be1238

consistent withσtotal from Ref. [6]. Numericallyσ≥1 also exhibits better convergence with this choice1239

for the central scale. Note thatσ≥2 is defined by inverting the cut on the second jet inσ1 and is not inde-1240

pendent of{σtotal, σ0, σ1}. Its percent uncertaintyδ≥2 naturally enters because of the theory correlation1241

model and for this purpose it should be taken at LO. Also note thatσ≥2 is different from the2-jet bin,σ2.1242

If σ2 is included one extends the matrix by an extra row/column, and uses as input that the uncertainties1243

in σtotal, σ≥1, σ≥2, σ≥3 are independent.1244

Whenσ2 is used in the analysis with additional vector-boson fusioncuts, one can determine the1245

uncertainties with the appropriateσ≥2 at NLO andσ≥3 at LO from MCFM [161]. To combine theσ21246

with additional vector boson fusion cuts with the0-jet and1-jet gluon-fusion bins, one treats the VBF1247

uncertainty as uncorrelated with those from gluon fusion, and assigns a 100% correlation between the1248

perturbative uncertainties of the two different gluon-fusion σ≥2s that appear in these computations.1249

Step 2 above also requires values forf0 andf1 as input. In the experimental analyses, the central1250

values forf0 andf1 effectively come from a full Monte Carlo simulation. By onlyusing relative quan-1251

tities, the different overall normalizations in the fixed-order calculation and the Monte Carlo drop out.1252

However, the values forf0 andf1 obtained from the fixed-order calculation can still be quitedifferent1253

November 18, 2011 – 11 : 26 DRAFT 70

from those in the Monte Carlo, because the fixed-order results incorporate NNLOαs corrections, while1254

the Monte Carlo includes some resummation as well as detector effects. A priori the values forf0,11255

obtained either way could be used as input for the uncertainty calculation in Step 2. One can cross check1256

that the two choices lead to similar results for the final uncertainties.1257

It is useful to illustrate this with a numerical example corresponding to Fig. 30, for which we1258

take pcutT = 30GeV and ηcut = 3.0. For MH = 165GeV, we haveσtotal = (8.76 ± 0.80) pb,1259

σ≥1 = (3.10 ± 0.61) pb, andσ≥2 = (0.73 ± 0.42) pb, corresponding to the relative uncertainties1260

δtotal = 9.1%, δ≥1 = 19.9%, andδ≥2 = 57%. Using these as inputs in Eq. (30) we find for the exclusive1261

jet cross sectionsδ(σ0) = 18%, δ(σ1) = 31% with correlations coefficientsρ(σ0, σtotal) = 0.79,1262

ρ(σ1, σtotal) = 0, andρ(σ0, σ1) = −0.50. We see thatσ0 andσ1 have a substantial negative correlation1263

because of the jet bin boundary they share. For the exclusivejet fractions using Eq. (31) we obtain1264

δ(f0) = 12% and δ(f1) = 33% with correlationsρ(f0, σtotal) = 0.42, ρ(f1, σtotal) = −0.28, and1265

ρ(f0, f1) = −0.84. The presence ofσtotal in the denominator of thefi’s yields a nonzero anticorrelation1266

for f1 andσtotal, and a decreased correlation forf0 andσtotal compared toσ0 andσtotal. In contrast to1267

these results, in method A one considers the direct scale variation in the exclusiveσ0,1 as in the left panel1268

of Fig. 30. Due to the cancellations between the perturbative series, this approach leads to unrealistically1269

small uncertainties (with the above inputsδ(σ0) = 3.2% andδ(σ1) = 8.3%), which is reflected in the1270

pinching of the bands in the left plot in Fig. 30.1271

As a final remark, we note that strictly speaking, it is somewhat inconsistent to use the relative1272

uncertainties forf0,1 from fixed order and apply them to the Monte Carlo predictionsfor f0,1. A more1273

sophisticated treatment would be to first correct the measurements for detector effects to truth-level using1274

Monte Carlo. In the second step, the corrected measurementsof σ0 andσ1 (with truth-level cuts) can1275

be directly compared to the available calculations, takinginto account the theoretical uncertainties as1276

described above. This also automatically makes a clean separation between experimental and theoretical1277

uncertainties. Given the importance and impact of the jet selection cuts, this is very desirable. It would1278

both strengthen the robustness of the extracted experimental limits and validate the theoretical description1279

of the jet selection.1280

5.3 Perturbative uncertainties in jet-veto efficiencies1281

A. Banfi, G. P. Salam, G. Zanderighi1282

In the context of Higgs-boson searches, it is common to splitthe Higgs production cross section1283

into different bins, corresponding to having a Higgs accompanied by 0, 1, 2 or more jets. Here we1284

concentrate on the 0-jet cross section, corresponding to having a Higgs and no jets with a transverse1285

momentum above a givenpcutT . Such a jet-veto condition plays a crucial role in the searchfor a Higgs1286

decaying into a pair ofW bosons, in that it suppresses the large background from top-antitop production.1287

We examine here the question of the theoretical uncertaintyin the prediction of the jet-veto efficiency. In1288

particular, we consider the ambiguity that arises in its calculation from a ratio of two cross sections that1289

are both known at next-to-next-to-leading order (NNLO).1290

In the following,Σ(pcutT ) will denote the 0-jet cross section, as a function of the jet transverse1291

momentum thresholdpcutT , whilst σ will denote the Higgs total cross section, without any jet veto. It1292

is also useful to consider the ratio of these cross sections,f0(pcutT ) = Σ(pcutT )/σ, which is commonly1293

referred to as the jet-veto efficiency, or the 0-jet fractionas in Section 5.2. Knowledge of this efficiency,1294

and its uncertainty, is important in interpreting measuredlimits on the Higgs cross section in the 0-jet1295

bin as a limit on the total Higgs production cross section.1296

BothΣ(pcutT ) andσ have a fixed-order perturbative expansion of the form

Σ(pcutT ) = Σ(0)(pcutT ) + Σ(1)(pcutT ) + Σ(2)(pcutT ) + . . . , (32a)

σ = σ(0) + σ(1) + σ(2) + . . . , (32b)

November 18, 2011 – 11 : 26 DRAFT 71

where the superscripti denotes the fact that the given contribution to the cross section is proportional to1297

αis relative to the Born cross section (of orderα2

s in the present case). Since no jets are present at the1298

Born level we haveΣ(0)(pcutT ) ≡ σ(0).1299

The state-of-the-art of fixed-order QCD predictions is NNLO, i.e. the calculation ofΣ2(pcutT ) and1300

σ2 with tools like FEHIP [129] andHNNLO [109]. Mixed QCD and electroweak corrections [151] are1301

also known, but we will not consider them here.1302

There is little ambiguity in the definition of the fixed order results for the total and jet-vetoed cross1303

sections, with the only freedom being, as usual, in the choice of the renormalization and the factorization1304

scale. However, given the expressions ofΣ andσ at a given perturbative order, there is some additional1305

freedom in the way one computes the jet-veto efficiency. For instance, at NNLO the efficiency can be1306

defined as1307

f(a)0 (pcutT ) ≡ Σ(0)(pcutT ) + Σ(1)(pcutT ) + Σ(2)(pcutT )

σ(0) + σ(1) + σ(2). (33)

This option is the most widely used, and may appear at first sight to be the most natural, insofar as one1308

keeps as many terms as possible both in the numerator and denominator. It corresponds to method A of1309

evaluating the uncertainty in the fraction of events in the zero-jet bin defined in Section 5.2.1.1310

However, other prescriptions are possible. For instance, since the zeroth order term off0(pcutT ) is1311

equal to1, one can argue that it is really only1− f0(pcutT ) that has a non-trivial perturbative series, given1312

by the ratio of the inclusive 1-jet cross section abovepcutT , σNLO1-jet (p

cutT ), to the total cross section, where1313

σNLO1-jet (p

cutT ) = σ(1) + σ(2) −

(Σ(1)(pcutT ) + Σ(2)(pcutT )

). (34)

Insofar as the 1-jet cross section is known only to NLO, in taking the ratio to the total cross section one1314

should also use NLO for the latter, so that an alternative prescription reads1315

f(b)0 (pcutT ) = 1−

σNLO1-jet (p

cutT )

σ(0) + σ(1). (35)

Finally, another motivated expression for the jet-veto efficiency is just the fixed order expansion up to1316

O(α2s) of Eq. ((33)), which can be expressed in terms of the LO and NLOinclusive jet cross sections1317

abovepcutT as follows1318

f(c)0 (pcutT ) = 1−

σNLO1-jet (p

cutT )

σ(0)+

σ(1)

(σ(0))2σLO

1-jet(pcutT ) . (36)

Prescriptions (a), (b) and (c) differ by terms of relative order α3s with respect to the Born level, i.e.1319

NNNLO. Therefore, the size of the differences between them is a way to estimate the associated theoret-1320

ical uncertainty that goes beyond the usual variation of scales.1321

Let us see how these three prescriptions fare in practice in the case of interest, namely Higgs1322

production at the LHC with 7 TeV centre-of-mass energy. We use MSTW2008NNLO parton distribution1323

functions [95] (even for LO and NLO predictions) withαs(MZ) = 0.11707 and three-loop running.1324

Furthermore, we use the largemtop approximation. We choose a Higgs mass of 145 GeV, and default1325

renormalization and factorization scales ofMH/2. We cluster partons into jets using the anti-kt jet1326

algorithm [116] withR = 0.5, which is the default jet definition for CMS. Switching toR = 0.4,1327

as used by ATLAS, has a negligible impact relative to the sizeof the uncertainties. We include jets1328

up to infinite rapidity, but have checked that the effect of a rapidity cut of4.5/5, corresponding to the1329

ATLAS/CMS acceptances, is also much smaller than other uncertainties discussed here.1330

The corresponding results for the jet-veto efficiencies over a wide range of values ofpcutT /MH1331

are shown in Fig. 32 (left). Each of the three prescriptions Eqs. (33), (35), (36) is presented together1332

with an associated uncertainty band corresponding to an independent variation of renormalization and1333

November 18, 2011 – 11 : 26 DRAFT 72

f 0(p

Tcut )

pTcut / MH

LHC, 7 TeV

HNNLO + MCFMMH/4 ≤ µR, µF ≤ MH

1/2 ≤ µR / µF ≤ 2

scheme (a)

scheme (b)

scheme (c)-0.2

0

0.2

0.4

0.6

0.8

1

0.01 0.1 1

f 0(p

Tcut )

pTcut / MZ

LHC, 7 TeV

DYNNLO + MCFMMZ/4 ≤ µR, µF ≤ MZ

1/2 ≤ µR / µF ≤ 2

scheme (a)

scheme (b)

scheme (c)-0.2

0

0.2

0.4

0.6

0.8

1

0.01 0.1 1

Fig. 32: Jet-veto efficiency for Higgs (left) and Z-boson production(right) using three different prescriptions for theNNLO expansion, see Eqs. (33), (35), (36). The bands are obtained by varying renormalization and factorizationscales independently around the central valueMH/2 (MZ/2) by a factor of two up and down (with the constraint12 ≤ µR/µF ≤ 2). NNLO predictions are obtained by suitably combining the total cross sections obtained withHNNLO [109] (DYNNLO [162]) with the 1-jet cross sectionσ1-jet(p

cutT ) computed withMCFM [163].

LO NLO NNLO

H [pb] 3.94+1.01−0.73 8.53+1.86

−1.34 10.5+0.8−1.0

Z [nb] 22.84+2.07−2.40 28.6+0.8

−1.2 28.6+0.4−0.4

Table 27: Cross sections for Higgs and Z-boson production in 7 TeV pp collisions, at various orders in perturbationtheory. The central value corresponds to the default scaleµR = µF =MH/2 (MZ/2), the error denotes the scalevariation whenµR andµF are varied independently by a factor two around the central value, with the constraint12 ≤ µR/µF ≤ 2.

factorization scalesMH/4 ≤ µR, µF ≤ MH (with the constraint12 ≤ µR/µF ≤ 2). The solid red1334

vertical line corresponds to a reference jet-veto of0.2MH ∼ 29 GeV, which is in the ballpark of the1335

value used by ATLAS and CMS to split the cross section in 0-, 1-and 2-jet bins (25GeV and30GeV1336

respectively). Several features can be observed: firstly, the three schemes lead to substantially different1337

predictions for the jet-veto efficiency, spanning a range from about 0.50 to 0.85 at the reference jet-veto1338

value. Furthermore, the uncertainty bands from the different schemes barely overlap, indicating that1339

scale uncertainties alone are a poor indicator of true uncertainties here. Finally the uncertainty bands’1340

widths are themselves quite different from one scheme to thenext.1341

The above features are all caused by the poor convergence of the perturbative series. In particular,1342

it seems that two classes of effects are at play here. Firstly, for pcutT << MH , there are large Sudakov1343

logarithmsαns ln

2n(pcutT /MH). These are the terms responsible for the drop in veto efficiency at lowpcutT1344

and the lack of a resummation of these terms to all orders is responsible for the unphysical increase in1345

veto efficiency seen at very lowpcutT (resummations of related observables are discussed in [157, 164]).1346

The second class of effects stems from the fact that the totalcross section has a very large NLO/LOK-1347

factor,∼ 2, with substantial corrections also at NNLO (see Table 27). The jet-veto efficiency is closely1348

connected to the 1-jet rate, for which the NNLO corrections are not currently known. It is conceivable1349

that they could be as large, in relative terms, as the NNLO corrections to the total cross section and our1350

different schemes for calculating the perturbative efficiency effectively take that uncertainty into account.1351

The reader may wonder whether it is really possible to attribute the differences between schemes1352

to the poor convergence of the total cross section. One cross-check of this statement is to examine the jet1353

November 18, 2011 – 11 : 26 DRAFT 73

veto efficiency for Z-boson production, where, with a central scale choiceµ = MZ/2, NLO corrections1354

to the total cross section are about25%, and the NNLO ones are a couple of percent (see Table 27). The1355

results for the jet-veto efficiency are shown in Fig. 32 (right). While overall uncertainties remain non-1356

negligible (presumably due to large Sudakov logarithms), the three expansion schemes do indeed give1357

almost identical results forpt,max/MZ = 0.2. This supports our interpretation that the poor total-cross1358

section convergence is a culprit in causing the differencesbetween the three schemes in the Higgs case.1359

To conclude, in determining the jet-veto efficiency for Higgs production, one should be aware that1360

fixed-order predictions depend significantly on the preciseform of the perturbative expansion used to1361

calculate the efficiency, Eqs. (33), (35) or (36). This uncertainty is not reflected in the scale-dependence1362

of the predictions, presumably in part because of the accidental cancellations between physically unre-1363

lated large Sudakov effects and large total-cross section corrections, a conclusion also reached in Sec. 5.21364

and Ref. [160].1365

5.4 The HiggsqT spectrum and its uncertainties1366

D. de Florian, G.Ferrera, M.Grazzini, D.Tommasini1367

5.4.1 Introduction1368

In this contribution we consider the transverse momentum (qT ) spectrum of the SM Higgs bosonH1369

produced by the gluon fusion mechanism. This observable is of direct importance in the experimental1370

search. A good knowledge of theqT spectrum can help to set up strategies to improve the statistical1371

significance. When studying theqT distribution of the Higgs boson in QCD perturbation theory it is1372

convenient to distinguish two regions of transverse momenta. In the large-qT region (qT ∼ MH), where1373

the transverse momentum is of the order of the Higgs boson massMH, perturbative QCD calculations1374

based on the truncation of the perturbative series at a fixed order inαs are theoretically justified. In this1375

region, theqT spectrum is known up to leading order (LO) [165] with the fulldependence of the masses1376

of the top and bottom quarks, and up to the next-to-leading order (NLO) [152, 153, 166] in the largeMt1377

limit.1378

In the small-qT region (qT << MH), where the bulk of the events is produced, the convergence1379

of the fixed-order expansion is spoiled by the presence of large logarithmic terms,αns ln

m(m2H/q

2T ). To1380

obtain reliable predictions, these logarithmically-enhanced terms have to be systematically resummed1381

to all perturbative orders [133, 167–177]. It is then important to consistently match the resummed and1382

fixed-order calculations at intermediate values ofqT , in order to obtain accurate QCD predictions for the1383

entire range of transverse momenta.1384

The resummation of the logarithmically enhanced terms is effectively (approximately) performed1385

by standard Monte Carlo event generators. In particular, MC@NLO [113] and POWEG [111] combine1386

soft-gluon resummation through the parton shower with the leading order (LO) result valid at largeqT ,1387

thus achieving a result with formal NLO accuracy.1388

The numerical programHqT [133] implements soft-gluon resummation up to NNLL accuracy1389

[178] combined with fixed-order perturbation theory up to NLO in the large-qT region [152]. The pro-1390

gram is used by the Tevatron and LHC experimental collaborations to reweight theqT spectrum of the1391

Monte Carlo event generators used in the analysis and is thusof direct relevance in the Higgs boson1392

search.1393

The programHqT is based on the transverse-momentum resummation formalismdescribed in1394

Refs. [133,176,177], which is valid for a generic process inwhich a high-mass system of non strongly-1395

interacting particles is produced in hadron–hadron collisions.1396

The phenomenological analysis presented in Ref. [133] has been recently extended in [157]. In1397

particular, we have implemented the exact value of the NNLO hard-collinear coefficientsHH(2)N com-1398

puted in Ref. [130,179], and the recently derived value of the NNLL coefficientA(3) [180].1399

November 18, 2011 – 11 : 26 DRAFT 74

Our calculation for theqT spectrum is implemented in the updated version of the numerical code1400

HqT, which can be downloaded from [103].1401

5.4.2 Transverse-momentum resummation1402

In this section we briefly recall the main points of the transverse-momentum resummation approach1403

proposed in Refs. [133,176,177], in the case of a Higgs bosonH produced by gluon fusion. As recently1404

pointed out in Ref. [177], the gluon fusionqT -resummation formula has a different structure than the1405

resummation formula forqq annihilation. The difference originates from the collinear correlations that1406

are a specific feature of the perturbative evolution of colliding hadron into gluon partonic initial states.1407

These gluon collinear correlations produce, in the small-qT region, coherent spin correlations between1408

the helicity states of the initial-state gluons and definiteazimuthal-angle correlations between the final-1409

states particles of the observed high-mass system. Both these kinds of correlations have no analogue for1410

qq annihilation processes in the small-qT region. In the case of Higgs boson production, beingH a spin-01411

scalar particle, the azimuthal correlations vanish and only gluon spin correlations are present [177].1412

We consider the inclusive hard-scattering process1413

h1(p1) + h2(p2) → H(MH, qT ) +X, (37)

whereh1 andh2 are the colliding hadrons with momentap1 andp2, MH andqT are the Higgs boson1414

mass and transverse momentum respectively, andX is an arbitrary and undetected final state.1415

According to the QCD factorization theorem the corresponding transverse-momentum differential1416

cross sectiondσH/dq2T can be written as1417

dσHdq2T

(qT ,MH, s) =∑

a,b

∫ 1

0dx1

∫ 1

0dx2 fa/h1

(x1, µ2F ) fb/h2

(x2, µ2F )

dσH,ab

dq2T(qT ,MH, s;αs(µ

2R), µ

2R, µ

2F ) ,

(38)wherefa/h(x, µ

2F ) (a = q, q, g) are the parton densities of the colliding hadronh at the factorization1418

scaleµF , dσH,ab/dq2T are the perturbative QCD partonic cross sections,s (s = x1x2s) is the square of1419

the hadronic (partonic) centre–of–mass energy, andµR is the renormalization scale.1420

In the region whereqT ∼ MH, the QCD perturbative series is controlled by a small expansion1421

parameter,αs(MH), and fixed-order calculations are theoretically justified.In this region, the QCD1422

radiative corrections are known up to NLO [152, 153, 166]. Inthe small-qT region (qT << MH),1423

the convergence of the fixed-order perturbative expansion is ruined by the presence of powers of large1424

logarithmic terms,αns ln

m(M2H/q

2T ) (with 1 ≤ m ≤ 2n − 1). To obtain reliable predictions these terms1425

have to be resummed to all orders.1426

We perform the resummation at the level of the partonic crosssection, which is decomposed as1427

dσH,ab

dq2T=dσ

(res.)H,ab

dq2T+dσ

(fin.)H,ab

dq2T. (39)

The first term on the right-hand side includes all the logarithmically-enhanced contributions, at small1428

qT , and has to be evaluated to all orders inαs. The second term is free of such contributions and can1429

thus be computed at fixed order in perturbation theory. To correctly take into account the kinematic1430

constraint of transverse-momentum conservation, the resummation program has to be carried out in the1431

impact parameter spaceb. Using the Bessel transformation between the conjugate variablesqT andb, the1432

resummed componentdσ(res.)H,ac can be expressed as1433

dσ(res.)H,ac

dq2T(qT ,MH, s;αs(µ

2R), µ

2R, µ

2F ) =

∫ ∞

0db

b

2J0(bqT ) WH

ac(b,MH, s;αs(µ2R), µ

2R, µ

2F ) , (40)

November 18, 2011 – 11 : 26 DRAFT 75

whereJ0(x) is the0th-order Bessel function. The resummation structure ofWHac can be organized in

exponential form considering the MellinN -momentsWHN of WH with respect to the variablez =M2

H/s

at fixedMH13,

WHN (b,MH;αs(µ

2R), µ

2R, µ

2F ) = HH

N

(MH, αs(µ

2R);M

2H/µ

2R,M

2H/µ

2F ,M

2H/Q

2)

× exp{GN (αs(µ2R), L;M

2H/µ

2R,M

2H/Q

2)} , (41)

were we have defined the logarithmic expansion parameterL ≡ ln(Q2b2/b20), andb0 = 2e−γE (γE =1434

0.5772... is the Euler number).1435

The scaleQ ∼MH, appearing in the right-hand side of Eq. (41), named resummation scale [133],parameterizes the arbitrariness in the resummation procedure. The form factorexp{GN} is universalandcontains all the termsαn

s Lm with 1 ≤ m ≤ 2n, that order-by-order inαs are logarithmically divergent

asb→ ∞ (or, equivalently,qT → 0). The exponentGN can be systematically expanded as

GN (αs, L;M2H/µ

2R,M

2H/Q

2) = L g(1)(αsL) + g(2)N (αsL;M

2H/µ

2R,M

2H/Q

2)

+αs

πg(3)N (αsL;M

2H/µ

2R,M

2H/Q

2) +O(αns L

n−2) (42)

where the termLg(1) resums the leading logarithmic (LL) contributionsαns L

n+1, the functiong(2)N1436

includes the NLL contributionsαns L

n [175], g(3)N controls the NNLL termsαns L

n−1 [178, 180] and so1437

forth. The explicit form of the functionsg(1), g(2)N andg(3)N can be found in Ref. [133].1438

The processdependentfunctionHHN does not depend on the impact parameterb and it includes

all the perturbative terms that behave as constants asb → ∞. It can thus be expanded in powers ofαs = αs(µ

2R):

HHN (MH, αs;M

2H/µ

2R,M

2H/µ

2F ,M

2H/Q

2) = σ(0)H (αs,MH)

[1 +

αs

πHH,(1)

N (M2H/µ

2F ,M

2H/Q

2)

+(αs

π

)2HH,(2)

N (M2H/µ

2R,M

2H/µ

2F ,M

2H/Q

2) +O(α3s )],

(43)

whereσ(0)H (αs,MH) is the partonic cross section at the Born level. The first order HH,(1)N [181] and the1439

second orderHH,(2)N [130, 179] coefficients in Eq. (43), for the case of Higgs boson production in the1440

large-Mt approximation, are known.1441

To reduce the impact of unjustified higher-order contributions in the large-qT region, the logarith-1442

mic variableL in Eq. (41), which diverges forb → 0, is actually replaced byL ≡ ln(Q2b2/b20 + 1

)1443

[133,182]. The variablesL andL are equivalent whenQb≫ 1 (i.e. at small valuesqT ), but they lead to a1444

different behaviour of the form factor at small values ofb. An important consequence of this replacement1445

is that, after inclusion of the finite component, we exactly recover the fixed-order perturbative value of1446

the total cross section upon integration of theqT distribution overqT .1447

The finite component of the transverse-momentum cross section dσ(fin.)H (see Eq. (39)) does not1448

contain large logarithmic terms in the small-qT region, it can thus be evaluated by truncation of the1449

perturbative series at a given fixed order.1450

In summary, to carry out the resummation at NLL+LO accuracy,we need the inclusion of the1451

functionsg(1), g(2)N , HH,(1)N , in Eqs. (42,43), together with the evaluation of the finite component at LO;1452

the addition of the functionsg(3)N andHH,(2)N , together with the finite component at NLO (i.e. atO(α2

s ))1453

13For the sake of simplicity we write the resummation formulaeonly for the specific case of the diagonal terms in the flavourspace. In general, the exponential is replaced by an exponential matrix with respect to the partonic indeces (a detaileddiscussionof the general case can be found in Ref. [133]).

November 18, 2011 – 11 : 26 DRAFT 76

leads to the NNLL+NLO accuracy. We point out that our best theoretical prediction (NNLL+NLO)1454

includes thefull NNLO perturbative contribution in the small-qT region plus the NLO correction at1455

large-qT . In particular, the NNLO result for the total cross section is exactly recovered upon integration1456

overqT of the differential cross sectiondσH/dqT at NNLL+NLO accuracy.1457

Finally we recall that the resummed form factorexp{GN (αs(µ2R), L)} has a singular behaviour,1458

related to the presence of the Landau pole in the QCD running coupling, at the values ofb where1459

αs(µ2R)L ≥ π/β0 (β0 is the first-order coefficient of the QCDβ function). To perform the inverse1460

Bessel transformation with respect to the impact parameterb a prescription is thus necessary. We follow1461

the regularization prescription of Refs. [183,184]: the singularity is avoided by deforming the integration1462

contour in the complexb space.1463

5.4.3 Results1464

The results we are going to present are obtained with an updated version of the numerical codeHqT1465

[103]. The new version of this code was improved with respectto the one used in Ref. [133]. The1466

main differences regard the implementation of the exact value of the second-order coefficientsHH,(2)N1467

computed in Ref. [130] and the use of the recently derived value of the coefficientA(3) [180], which1468

contributes to NNLL accuracy (the results in Ref. [133] wereobtained by using theA(3) value from1469

threshold resummation [185]). Detailed results for theqT spectrum at the Tevatron and the LHC are1470

presented in Ref. [157]. Here we focus on the uncertainties of the qT spectrum at the LHC.1471

The calculation is performed strictly in the large-Mt approximation. Effects beyond this approxi-1472

mation are discussed elsewhere in this report.1473

The hadronicqT cross section at NNLL+NLO (NLL+LO) accuracy is computed by using NNLO1474

(NLO) parton distributions functions (PDFs) withαs(µ2R) evaluated at 3-loop (2-loop) order. We use the1475

MSTW2008 parton densities unless otherwise stated.1476

As discussed in Sect. 5.4.2, the resummed calculation depends on the factorization and renormal-1477

ization scales and on the resummation scaleQ. Our convention to compute factorization and renormal-1478

ization scale uncertainties is to consider independent variations ofµF andµR by a factor of two around1479

the central valuesµF = µR = MH (i.e. we consider the rangeMH/2 ≤ {µF , µR} ≤ 2MH), with the1480

constraint0.5 ≤ µF/µR ≤ 2. Similarly, we follow Ref. [133] and chooseQ = MH/2 as central value1481

of the resummation scale, considering scale variations in the rangeMH/4 < Q < MH.1482

We focus on the uncertainties on thenormalizedqT spectrum (i.e.,1/σ× dσ/dqT ). As mentioned1483

in the introduction, the typical procedure of the experimental collaborations is to use the information1484

on the total cross section [6] to rescale the best theoretical predictions of Monte Carlo event generators,1485

whereas the NNLL+NLO result of our calculation, obtained with the public programHqT, is used to1486

reweight the transverse-momentum spectrum of the Higgs boson obtained in the simulation. Such a1487

procedure implies that the important information providedby the resummed NNLL+NLO spectrum is1488

not its integral, i.e. the total cross section, but itsshape. The sources of uncertainties on the shape of1489

the spectrum are essentially the same as for the inclusive cross section: the uncertainty from missing1490

higher-order contributions, estimated through scale variations, PDF uncertainties, and the uncertainty1491

from the use of the large-Mt approximation, that are discussed elsewhere in this report. One additional1492

uncertainty in theqT spectrum that needs be considered comes from Non-Perturbative (NP) effects.1493

It is known that the transverse-momentum distribution is affected by NP effects, which become1494

important asqT becomes small. A customary way of modelling these effects isto introduce an NP1495

transverse-momentum smearing of the distribution. In the case of resummed calculations in impact1496

parameter space, the NP smearing is implemented by multiplying theb-space perturbative form factor1497

by an NP form factor. The parameters controlling this NP formfactor are typically obtained through a1498

comparison to data. Since there is no evidence for the Higgs boson yet, the way to fix the NP form factor1499

is somewhat arbitrary. Here we follow the procedure adoptedin Ref. [133, 157], and we multiply the1500

November 18, 2011 – 11 : 26 DRAFT 77

resummed form factor in Eq. (40) by a gaussian smearingSNP = exp{−gb2}, where the parameterg is1501

taken in the range (g = 1.67 − 5.64 GeV2) suggested by the study of Ref. [186]. The above procedure1502

can give us some insight on the quantitative impact of these NP effects on the Higgs boson spectrum.1503

In Fig. 33 (left panels) we compare the NNLL+NLO shape uncertainty as coming from scale1504

variations (solid lines) to the NP effects (dashed lines) for MH=120 GeV andMH=165 GeV . The1505

bands are obtained by normalizing each spectrum to unity, and computing the relative difference with1506

respect to the central normalized prediction obtained withthe MSTW2008 NNLO set (withg = 0). In1507

other words, studying uncertainties on the normalized distribution allows us to assess the true uncertainty1508

in the shape of the resummedqT spectrum.1509

We see that, both forMH = 120 GeV and forMH = 165 GeV the scale uncertainty ranges from1510

+5% − 3% in the region of the peak to±5% at qT ∼ 70 GeV. The impact of NP effects ranges from1511

about 10% to 20% in the region below the peak, is about3−4% for qT ∼ 20 GeV, and quickly decreases1512

asqT increases. We conclude that the uncertainty from unknown NPeffects is smaller than the scale1513

uncertainty, and is comparable to the latter only in the verysmallqT region.1514

The impact of PDF uncertainties at68% CL on the shape of theqT spectrum is studied in Figs. 331515

(right panels). By evaluating PDF uncertainties with MSTW2008 NNLO PDFs we see that the uncer-1516

tainty is at the±1 − 2% level. The use of different PDF sets affects not only the absolute value of1517

the NNLO cross section (see e.g. Ref. [187]) but also the shape of theqT spectrum. The predictions1518

obtained with NNPDF 2.1 PDFs are in good agreement with thoseobtained with the MSTW2008 set1519

and the uncertainty bands overlap over a wide range of transverse momenta, both forMH = 120 GeV1520

andMH = 165 GeV . On the contrary, the prediction obtained with the ABKM09 NNLO set is softer1521

and the uncertainty band does not overlap with the MSTW2008 band. This behaviour is not completely1522

unexpected: when the Higgs boson is produced at large transverse momenta, larger values of Bjorken1523

x are probed, where the ABKM gluon is smaller than MSTW2008 one. The JR09 band shows a good1524

compatibility with the MSTW2008 result where the uncertainty is however rather large.1525

5.5 Monte Carlo and resummation for exclusive jet bins1526

I. W. Stewart, F. Stöckli, F. J. Tackmann, W. J. Waalewijn1527

5.5.1 Overview1528

In this section we discuss the use of predictions for exclusive jet cross sections that involve resummation1529

for the jet-veto logarithms,ln(pcut/MH), induced by the jet cut parameterpcut shown in Eq. (18) of1530

Sec. 5.2. It is common practice to account for thepcut dependence in exclusiveH + 0 jet cross sections1531

using Monte Carlo programs such as Pythia, MC@NLO, or POWHEG, which include a resummation1532

of at least the leading logarithms (LL). One may also improvethe accuracy of spectrum predictions by1533

reweighting the Monte Carlo to resummed predictions for theHiggsqT spectrum (see Sec. 5.4), which1534

starts to differ from the jet-veto spectrum atO(α2s). The question then remains how to assess theoretical1535

uncertainties, and three methods (A, B, and C) were outlinedin Sec. 5.2.1536

In this section we consider assessing the perturbative uncertainties when using resummed predic-1537

tions for variablespcut that implement a jet veto, corresponding to method C. An advantage of using1538

these resummed predictions with method C is that they contain perturbation theory scale parameters1539

which allow for an evaluation of two components of the theoryerror, one which is 100% correlated1540

with the total cross section (as in method A), and one relatedto the presence of the jet-bin cut which is1541

anti-correlated between neighboring jet bins (as in methodB). Our discussion of the correlation matrix1542

obtained from method C follows Ref. [160].1543

We consider two choices for the jet-veto variable, the standard pjetT variable with a rapidity cut1544

|η| ≤ ηcut (using anti-kT withR = 0.5), and the beam thrust variable [188], which is a rapidity-weighted1545

November 18, 2011 – 11 : 26 DRAFT 78

Fig. 33: Uncertainties in the shape of theqT spectrum: scale uncertanties compared with NP effects (left panels);PDF uncertainties (right panels).

HT , defined as1546

Tcm =∑

k

|~pTk|e−|ηk | =∑

k

(Ek − |pzk|) . (44)

The sum here is over all objects in the final state except the Higgs decay products, and can in principle1547

be considered over particles, topo-clusters, or jets with asmallR parameter. We make use of resummed1548

predictions forH + 0 jets from gluon fusion at next-to-next-to-leading logarithmic order with NNLO1549

fixed order precision (NNLL+NNLO) from Ref. [164]. The resulting cross sectionσ0(T cutcm ) has the jet1550

veto implemented by a cutTcm ≤ T cutcm . This cross section contains a resummation of large logarithms at1551

two orders beyond standard LL parton shower programs, and also includes the correct NNLO corrections1552

for σ0(T cutcm ) for any cut.1553

A similar resummation for the case ofpjetT is not available. Instead, we use MC@NLO and1554

reweight it to the resummed predictions inTcm including uncertainties and then use the reweighted1555

Monte Carlo sample to obtain cross section predictions for the standard jet veto,σ0(pcutT ). We will refer1556

to this as the reweighted NNLL+NNLO result. Since the Monte Carlo here is only used to provide a1557

transfer matrix betweenTcm andpjetT , and both variables implement a jet veto, one expects that most of1558

the improvements from the higher-order resummation are preserved by the reweighting. However, we1559

caution that this is not equivalent to a complete NNLL+NNLO result for thepcutT spectrum, since the1560

reweighting may not fully capture effects associated with the choice of jet algorithm and other effects1561

that enter at this order forpcutT . The dependence on the Monte Carlo transfer matrix also introduces an1562

November 18, 2011 – 11 : 26 DRAFT 79

additional uncertainty, which should be studied and is not included in our numerical results below. (We1563

have checked that varying the fixed-order scale in MC@NLO betweenµ = MH/4 andµ = 2MH has a1564

very small effect on the reweighted results.) The transfer matrix is obtained at the parton level, without1565

hadronization or underlying event, since we are reweighting a partonic NNLL+NNLO calculation. In all1566

our results we consistently use MSTW2008 NNLO PDFs.1567

In Sec. 5.5.2 we discuss the determination of perturbative uncertainties in the resummed calcula-1568

tions (method C), and compare them with those at NNLO obtained from a direct exclusive scale variation1569

(method A) and from combined inclusive scale variation (method B) for bothσ0(pcutT ) andσ0(T cutcm ). In1570

Sec. 5.5.3 we compare the predictions for the 0-jet bin eventfraction at different levels of resummation,1571

comparing results from NNLO, MC@NLO, and the (reweighted) NNLL+NNLO analytic results.1572

5.5.2 Uncertainties and Correlations from Resummation1573

The resummedH + 0-jet cross section predictions of Ref. [164] follow from a factorization theorem1574

for the0-jet cross section [188],σ0(T cutcm ) = H Igi Igj ⊗ Sfifj, whereH contains hard virtual effects,1575

the Is andS describe the veto-restricted collinear and soft radiation, and thefs are standard parton1576

distributions. Fixed-order perturbation theory is carried out at three scales, a hard scaleµ2H ∼ M2H in1577

H, and beam and soft scalesµ2B ∼ MHT cutcm andµ2S ∼ (T cut

cm )2 for I andS, and are then connected by1578

NNLL renormalization group evolution that sums the jet-veto logarithms, which are encoded in ratios1579

of these scales. The perturbative uncertainties can be assessed by considering two sources: i) an overall1580

scale variation that simultaneously varies{µH , µB , µS} up and down by a factor of two which we denote1581

by ∆H0, and ii) individual variations ofµB or µS that each hold the other two scales fixed [164], whose1582

envelope we denote by the uncertainty∆SB. Here∆H0 is dominated by the same sources of uncertainty1583

as the total cross sectionσtotal, and hence should be considered 100% correlated with its uncertainty1584

∆total. The uncertainty∆SB is only present due to the jet bin cut, and hence gives the∆cut uncertainty1585

discussed in Sec. 5.2 that is anti-correlated between neighboring jet bins.1586

If we simultaneously consider the cross sections{σ0, σ≥1} then the full correlation matrix withmethod C is

C =

(∆2

SB −∆2SB

−∆2SB ∆2

SB

)+

(∆2

H0 ∆H0 ∆H≥1

∆H0∆H≥1 ∆2H≥1

), (45)

where∆H≥1 = ∆total −∆H0 encodes the 100% correlated component of the uncertainty for the(≥ 1)-1587

jet inclusive cross section. Computing the uncertainty inσtotal gives back∆total. Eq. (45) can be1588

compared to the corresponding correlation matrix from method A, which would correspond to taking1589

∆SB → 0 and obtaining the analog of∆H0 by up/down scale variation without resummation (µH =1590

µB = µS). It can also be compared to method B, which would correspondto taking∆SB → ∆≥1 and1591

∆H≥1 → 0, such that∆H0 → ∆total. Using method C captures both of the types of uncertainty that1592

appear in methods A and B. Note that the numerical dominance of ∆2SB over∆H0∆H≥1 in the 0-jet1593

region is another way to justify the preference for using method B when given a choice between methods1594

A and B. For example, forpcutT = 30GeV and |ηjet| ≤ 5.0 we have∆2SB = 0.17 and∆H0∆H≥1 =1595

0.02. From Eq. (45) it is straightforward to derive the uncertainties and correlations in method C when1596

considering the0-jet event fraction,{σtotal, f0}, in place of the jet cross sections. We will discuss results1597

for f0(pcutT ) andf0(T cutcm ) in Sec. 5.5.3 below.1598

In Fig. 34 we show the uncertainties∆SB (light green) and∆H0 (medium blue) as a function of1599

the jet-veto variable, as well as the combined uncertainty adding these components in quadrature (dark1600

orange). From the figure we see that theµH0 dominates at large values where the veto is turned off and1601

we approach the total cross section, and that the jet-cut uncertainty∆SB dominates for the small cut1602

values that are typical of experimental analyses with Higgsjet bins. The same pattern is observed in the1603

left panel which directly uses the NNLL+NNLO predictions for T cutcm , and the right panel which shows1604

the result from reweighting these predictions topcutT as explained above.1605

November 18, 2011 – 11 : 26 DRAFT 80

0

0

10

10

20

20

30

30 40 50 60 70 80 90 100

−10

−20

−30

T cutcm [GeV]

δσ

0[%

]

∆H0

∆SB

√

∆2H0+∆2

SB

√s=7 TeV

MH =165 GeV

0

0

10

10

20

20

30

30 40 50 60 70 80 90 100

−10

−20

−30

pcutT [GeV]

δσ

0[%

]

∆H0

∆SB

√

∆2H0+∆2

SB

|ηjet|≤5.0

√s=7 TeV

MH =165 GeV

Fig. 34: Relative uncertainties for the 0-jet bin cross section fromresummation at NNLL+NNLO for beam thrustTcm on the left andpjetT on the right.

0

0

10

10

20

20

30

30

40

40 50

−10

−20

−30

−40

T cutcm [GeV]

δσ

0[%

]

NNLL+NNLO

NNLO (methodA)

NNLO (methodB)

√s=7 TeV

MH =165 GeV

0

0

10

10

20

20

30

30

40

40 50

−10

−20

−30

−40

pcutT [GeV]

δσ

0[%

]

NNLO (methodA)

NNLO (methodB)

rew.NNLL+NNLO

|ηjet|≤5.0

√s=7 TeV

MH =165 GeV

Fig. 35: Comparison of uncertainties for the 0-jet bin cross sectionfor beam thrustTcm on the left andpjetT on theright. Results are shown at NNLO using methods A and B (directexclusive scale variation and combined inclusivescale variation as discussed in Sec. 5.2), and for the NNLL+NNLO resummed result (method C). All curves arenormalized relative to the NNLL+NNLO central value.

A comparison of the uncertainties for the 0-jet bin cross section from methods A (medium green),1606

B (light green), and C (dark orange) is shown in Fig. 35, wherethe results are normalized to the highest-1607

order result to better show the relative differences and uncertainties. The NNLO uncertainties in methods1608

A and B are computed in the manner discussed in Sec. 5.2. The uncertainties in method C are the1609

combined uncertainties from resummation given by√

∆2H0 +∆2

SB in Fig. 34. In the left panel we1610

useT cutcm as jet-veto variable and full results for the NNLO and NNLL+NNLO cross sections, while in1611

the right panel we usepcutT as jet-veto variable with the full NNLO and the reweighted NNLL+NNLO1612

results. One observes that the resummation of the large jet-veto logarithms lowers the cross section in1613

both cases. For cut values& 25GeV the relative uncertainties in the resummed result and the reduction1614

in the resummed central value compared to NNLO are similar for both jet-veto variables. One can also1615

see that the NNLO uncertainties from method B are more consistent with the higher order NNLL+NNLO1616

resummed results than those in method A.1617

From Fig. 35 we observe that the uncertainties in method C including resummation (dark orange1618

bands) are reduced by about a factor of two compared to those in method B (light green bands). Since the1619

zero-jet bin plays a crucial role in theH → WW channel for Higgs searches, and these improvements1620

will also be reflected in uncertainties for the one-jet bin, the improved theoretical precision obtained with1621

November 18, 2011 – 11 : 26 DRAFT 81

method A method B method C

δσ0(pcutT ) 3% 19% 9%

δσ≥1(pcutT ) 19% 19% 14%

ρ(σtotal, σ0) 1 0.78 0.15ρ(σtotal, σ≥1) 1 0 0.65ρ(σ0, σ≥1) 1 −0.63 −0.65

δf0(pcutT ) 6% 13% 9%

δf≥1(pcutT ) 10% 21% 11%

ρ(σtotal, f0) −1 0.43 −0.38ρ(σtotal, f≥1) 1 −0.43 0.38

Table 28: Example of relative uncertaintiesδ and correlationsρ obtained for the LHC at7TeV for pcutT = 30GeV

and |ηjet| ≤ 5.0. (Method A is shown for illustration only and should not be used for the reasons discussed inSec. 5.2.)

method C has the potential to be quite important.1622

To appreciate the effects of the different methods on the correlation matrix we consider as an1623

example the results forpcutT = 30GeV and |ηjet| ≤ 5.0. The inclusive cross sections areσtotal =1624

(8.76 ± 0.80) pb at NNLO, andσ≥1 = (3.10 ± 0.61) pb at NLO. The relative uncertainties and corre-1625

lations at these cuts for the three methods are shown in Table28. The numbers for the cross sections1626

are also translated into the equivalent results for the event fractions,f0(pcutT ) = σ0(pcutT )/σtotal and1627

f≥1(pcutT ) = σ≥1(p

cutT )/σtotal. Note that method A should not be used for the reasons discussed in detail1628

in Sec. 5.2, which are related to the lack of a contribution analogous to∆SB in this method, and the1629

resulting very small and underestimatedδσ0. In methods B and C we see, as expected, thatσ0 andσ≥11630

have a substantial anti-correlation due to the jet-bin boundary they share.1631

In Sec. 5.2, method B was discussed for{σtotal, σ0, σ1}, where we also account for the jet-bin1632

boundary betweenσ1 andσ≥2. The method C results discussed here so far are relevant for the jet-bin1633

boundary betweenσ0 andσ≥1. To also separateσ≥1 into a one-jet binσ1 and aσ≥2 one can simply1634

use method B for this boundary by treating∆≥2 as uncorrelated with the total uncertainty∆≥1 from1635

method C. Once it becomes available one can also use a resummed prediction with uncertainties for this1636

boundary with method C.1637

5.5.3 Comparison of NNLO, MC@NLO, and Resummation at NNLL+NNLO1638

In this Section we compare the results for the0-jet event fractionf0 from different theoretical methods1639

including various levels of logarithmic resummation. We use the event fraction for this comparison since1640

it is the quantity used in experimental analyses and what is typically provided by the Monte Carlo. We1641

compare three different results using bothpjetT and beam thrust as jet-veto variables:1642

1. Fixed-order perturbation theory at NNLO without resummation, where the uncertainties are eval-1643

uated using method B.1644

2. MC@NLO, which includes the LL (and partial NLL) resummation provided by the parton shower.1645

For the uncertainties we use the relative NNLO uncertainties evaluated using method B.1646

3. Resummation at NNLL+NNLO, with the uncertainties provided by the resummation (method C).1647

For beam thrust we directly compare to the full result at thisorder. ForpjetT we use the resummed1648

beam-thrust result reweighted topjetT using Monte Carlo as explained at the beginning of this1649

section.1650

The comparison forf0(T cutcm ) is shown in Fig. 36 and forf0(p

jetT ) in Fig. 37. The left panels in1651

each case show the0-jet event fractions, and the right panels normalize these same results to the highest-1652

November 18, 2011 – 11 : 26 DRAFT 82

order curve to illustrate the relative differences and uncertainties. Since the parton shower includes the1653

resummation of the leading logarithms, we expect the MC@NLOresults to show a similar behavior than1654

the NNLL resummed result, which is indeed the case. For both variables, the MC@NLO central value1655

is near the upper edge of the NNLL+NNLO uncertainty band (dark orange band). From Fig. 37 we1656

see that the uncertainties assigned to the MC@NLO results via method B (light blue band) include the1657

NNLL+NNLO central value forf0(pcutT ).14 We also see that the uncertainties forf0(pcutT ) in method C1658

are reduced by roughly a factor of two compared to MC@NLO withmethod B. This is the analog of1659

the observation that we made forσ0(pcutT ) in Fig. 35 when comparing NNLO method B and method C1660

uncertainties.1661

From theδf0 plots in Figs. 36 and 37 we observe that the impact of the resummation on the1662

NNLL+NNLO central value compared to the NNLO central value without resummation is similar for1663

both jet-veto variables for cut values& 25GeV. In this region the MC@NLO central value lies closer1664

to the NNLO than the NNLL+NNLO for both variables. However, it is hard to draw conclusions on the1665

impact of resummation by only comparing MC@NLO and NNLO since they each contain a different1666

set of higher-order corrections beyond NLO. For smaller cutvalues. 25GeV, the two variables start1667

to behave differently, and the NNLL+NNLO resummation has a larger impact relative to NNLO when1668

cutting onTcm than when cutting onpcutT .1669

To understand these features in more detail one has to take into account two different effects arising1670

from the two ways in which these jet-veto variables differ. First, the objects are weighted differently1671

according to their rapidity in the two jet-veto variables. ForTcm the particles are weighted bye−|η|, while1672

for pjetT no weighting inη takes place. Second, the way in which the cut restriction is applied to the objects1673

in the final state is different. By cutting onTcm, the restriction is applied to the sum over all objects1674

(either particles or jets) in the final state, while by cutting on the leadingpjetT the restriction is applied to1675

the maximum value of all objects (after an initial grouping into jets with small radius). To disentangle1676

these two effects we consider two additional jet-veto variables: HT which inclusively sums over all1677

object |pT |s in the same way asTcm does but without the rapidity weighting, and alsoTjet, the largest1678

individual beam thrust of any jet, which has the same object treatment aspjetT but with the beam-thrust1679

rapidity weighting. The effect of the different rapidity weighting already appears in the LL series for the1680

jet veto, i.e., atO(αs) the coefficient of the leading double logarithm is a factor oftwo larger forpcutT than1681

for T cutcm , σ0(pcutT ) ∝ 1−6αs/π ln

2(pcutT /MH)+ . . . versusσ0(T cutcm ) ∝ 1−3αs/π ln

2(T cutcm /MH)+ . . ..1682

In contrast, the LL series is the same forHT andpjetT , and forTcm andTjet. The larger logarithms for1683

pcutT thanT cutcm are reflected by the fact thatσ0(pcutT ) is noticeably smaller thanσ0(T cut

cm ) at equal cut1684

values. For the same type of object restriction the effect ofthe resummation follows the pattern expected1685

from the leading logarithms: The resummation has a larger impact forpjetT thanTjet, and also forHT1686

thanTcm. On the other hand, a cut on the (scalar) sum of objects is always a stronger restriction than the1687

same cut on the maximum value of all objects, since the formerrestricts wide-angle radiation more. As1688

a result the resummation has more impact onTcm than onTjet, and also onHT than onpjetT . From what1689

we observe in Figs. 36 and 37, these two competing effects appear to approximately balance each other1690

for pjetT andTcm for cut values& 25GeV.1691

To summarize, our results provide an important validation of using method B with relative uncer-1692

tainties obtained at NNLO and applying these to the event fractions obtained from NLO Monte Carlos.1693

While we have only compared to MC@NLO, we expect the same to betrue for POWHEG as well. By1694

reweighting the Monte Carlo to the NNLL+NNLO result the uncertainties in the predictions can be fur-1695

ther reduced to those obtained from the higher-order resummation using method C, and this provides an1696

important avenue for improving the analysis beyond method B. It would also be very useful to investigate1697

experimentally the viability of usingTjet as the jet-veto variable, by only summing over the jet (or jets)1698

14The blue uncertainty bands for the MC@NLO curves are cut off at very small cut values only because the NNLO crosssection diverges there and so its relative uncertainties are no longer meaningful. This happens for cut values well below theregion of experimental interest.

November 18, 2011 – 11 : 26 DRAFT 83

00

1

10 20 30 40 50

0.2

0.4

0.6

0.8

Tcm [GeV]

f0(T

cut

cm)

NNLL+NNLO

NNLO (methodB)

MC@NLO (methodB)

√s=7 TeV

MH =165 GeV

0

0

10

10

20

20

30

30

40

40 50

−10

−20

−30

−40

T cutcm [GeV]

δf

0[%

]

NNLL+NNLO

NNLO (methodB)

MC@NLO (methodB)

√s=7 TeV

MH =165 GeV

Fig. 36: Comparison of the0-jet fraction for different levels of resummation using beam thrust as the jet-vetovariable. Results are shown at NNLO (using method B uncertainties), MC@NLO (using the relative NNLOuncertainty from method B), and for the analytic NNLL+NNLO resummed result.

00

1

10 20 30 40 50

0.2

0.4

0.6

0.8

pcutT [GeV]

f0(p

cut

T)

NNLO (methodB)

MC@NLO (methodB)

rew.NNLL+NNLO

|ηjet|≤5.0

√s=7 TeV

MH =165 GeV

0

0

10

10

20

20

30

30

40

40 50

−10

−20

−30

−40

pcutT [GeV]

δf

0[%

]

NNLO (methodB)

MC@NLO (methodB)

rew.NNLL+NNLO

|ηjet|≤5.0

√s=7 TeV

MH =165 GeV

Fig. 37: Comparison of the0-jet fraction for different levels of resummation usingpjetT with |ηjet| ≤ 5.0 as the jet-veto variable. Results are shown at NNLO (using method B uncertainties), MC@NLO (using the relative NNLOuncertainty from method B), and for the reweighted NNLL+NNLO resummed result.

with the largest individual beam thrust, as this would combine the advantages of a jet-based variable with1699

the theoretical control provided by the beam-thrust resummation.1700

November 18, 2011 – 11 : 26 DRAFT 84

6 VBF production mode151701

The production of a Standard Model Higgs boson in association with two hard jets in the forward and1702

backward regions of the detector, frequently quoted as the “vector-boson fusion” (VBF) channel, is a1703

cornerstone in the Higgs-boson search both in the ATLAS [189] and CMS [190] experiments at the1704

LHC. Higgs-boson production in the VBF channel plays also animportant role in the determination of1705

Higgs-boson couplings at the LHC (see e.g. Ref. [10]).1706

The production of a Higgs boson + 2 jets receives two contributions at hadron colliders. The first1707

type, where the Higgs boson couples to a weak boson that linkstwo quark lines, is dominated byt-1708

andu-channel-like diagrams and represents the genuine VBF channel. The hard jet pairs have a strong1709

tendency to be forward-backward directed in contrast to other jet-production mechanisms, offering a1710

good background suppression. The second type of diagrams are actually a contribution toWH andZH1711

production, with theW/Z decaying into a pair of jets.1712

In the previous report [6], state-of-the-art predictions and error estimates for the total cross sections1713

for pp → H+2 jets have been compiled. These were based on an (approximate) NNLO calculation [191]1714

of the total VBF cross section based on the structure-function approach and on calculations of the elec-1715

troweak (EW) corrections by the Monte-Carlo programs HAWK [192–194] and VBFNLO [195, 196].1716

The EW corrections where simply included as a multiplicative correction factor to the NNLO QCD1717

prediction.1718

In this contribution we consider predictions for cross sections with cuts and distributions. This is1719

particularly interesting for VBF, as cuts on the tagging jets are used to suppress events from Higgs + 2 jet1720

production via gluon fusion and other backgrounds and to enhance the VBF signal. Since no NNLO cal-1721

culation for VBF exists so far for differential distributions or cross sections with cuts, we use NLO1722

codes. We also provide results for NLO-QCD corrections + parton shower, as generated using the1723

POWHEG [111] method and implemented in the POWHEG BOX code [159].1724

6.1 Theoretical framework1725

The results presented in Section 6.3 have been obtained withthe Monte Carlo programs HAWK and1726

VBFNLO, which include both QCD and EW NLO corrections, and with POWHEG, a method to inter-1727

face QCD NLO calculations with parton showers. Some detailson these codes are given in the following.1728

6.1.1 HAWK1729

The Monte Carlo event generator HAWK [192–194] had already been described in Ref. [6]. Since then,1730

it has been extended to the processespp → WH → νl l H andpp → ZH → l−l+H/νlνlH [?] (see1731

Section 7.1). Here we summarize its most important featuresfor the VBF channel. HAWK includes the1732

complete NLO QCD and EW corrections and all weak-boson fusion and quark–antiquark annihilation1733

diagrams, i.e.t-channel andu-channel diagrams with VBF-like vector-boson exchange ands-channel1734

Higgs-strahlung diagrams with hadronic weak-boson decay,as well as all interferences.1735

For the results presented below,s-channel contributions and interferences have been switched off.1736

Their contribution is below1% once VBF cuts are applied. While HAWK allows to include contributions1737

of b-quark PDFs and final-stateb quarks at LO, these contributions have been switched off as well. With1738

VBF cuts, they can amount to about2%. HAWK allows for an on-shell Higgs boson or for an off-shell1739

Higgs boson (with optional decay into a pair of gauge singlets). For the virtuality of the off-shell Higgs1740

boson the usual Breit-Wigner distribution1741

1

π

MH ΓH(M2 −M2

H

)2+ (MH ΓH)2

(46)

15A. Denner, S. Farrington, C. Hackstein, C. Oleari, D. Rebuzzi (eds.); S. Dittmaier, A. Mück, S. Palmer, B. Quayle

November 18, 2011 – 11 : 26 DRAFT 85

is used. This form results from the gauge-invariant expansion about the complex Higgs-boson pole and is1742

properly normalized. As any other parametrization, it becomes unreliable for large Higgs-boson masses,1743

where the Higgs-boson width gets large and contributions far from the pole become sizeable.1744

6.1.2 VBFNLO1745

VBFNLO [197, 198] is a parton-level Monte Carlo event generator that can be used to simulate vector-1746

boson fusion, double and triple vector-boson production inhadronic collisions at next-to-leading order1747

in the strong coupling constant, as well as Higgs-boson plustwo jet production via gluon fusion at the1748

one-loop level. For Higgs-boson production via VBF, both the NLO QCD and electroweak corrections1749

to thet-channel can be included [196, 199] in the Standard Model andthe (complex) MSSM16, and the1750

NLO QCD corrections are included for anomalous couplings between the Higgs and a pair of vector1751

bosons.1752

VBFNLO can also simulate the Higgs decaysH → γγ, µ+µ−, τ+τ−,bb in the narrow-width ap-1753

proximation, either taking the appropriate branching ratios from an input SLHA file or calculating them1754

internally. The Higgs-boson decaysH → W+W− → l+νll−ν l andH → ZZ → l+l−l+l−, l+l−νlνl1755

are calculated using a Breit-Wigner distribution for the Higgs boson and the full matrix element for the1756

H → 4f decay.1757

For the results presented here, a modified version of VBFNLO was used that simulated a Higgs-1758

boson decay with a branching ratio of 1 and a Breit-Wigner distribution (46) for the virtuality of the1759

off-shell Higgs boson.1760

6.1.3 POWHEG1761

The POWHEG method is a prescription for interfacing NLO calculations with parton-shower gener-1762

ators, like HERWIG and PYTHIA. It was first presented in Ref. [111], and was described in great1763

detail in Ref. [112]. In Ref. [200], Higgs-boson productionin VBF has been implemented in the frame-1764

work of the POWHEG BOX [159], a computer framework that implements in practice the theoretical1765

construction of Ref. [112].1766

All the details of the implementation can be found in Ref. [200]. Here we briefly recall that, in the1767

calculation of the partonic matrix elements, all partons have been treated as massless. This gives rise to1768

a different treatment of quark flavours for diagrams where aZ boson or aW boson is exchanged in thet1769

channel. In fact, for allZ-exchange contributions, theb-quark is included as an initial and/or final-state1770

massless parton. ForW-exchange contributions, no initialb-quark has been considered, since it would1771

have produced mostly at quark in the final state, that would have been misleadingly treated as massless.1772

The Cabibbo-Kobayashi-Maskawa (CKM) matrixVCKM has been taken as1773

VCKM =

d s buct

0.9748 0.2225 0.00360.2225 0.9740 0.0410.009 0.0405 0.9992

.

(47)

The Higgs-boson virtualityM2 has been generated distributed according to1774

1

π

M2 ΓH/MH(M2 −M2

H

)2+ (M2 ΓH/MH)2

, (48)

with fixed decay widthΓH.1775

As a final remark, we recall that the renormalizationµR and factorizationµF scales have been1776

taken equal to the transverse momentum of the radiated parton, during the generation of radiation, as1777

16For more details see Section 12.3.4.

November 18, 2011 – 11 : 26 DRAFT 86

the POWHEG method requires. The transverse momentum of the radiated parton is taken, in the case1778

of initial-state radiation, as exactly equal to the transverse momentum of the parton with respect to the1779

beam axis. For final-state radiation one takes instead1780

p2T = 2E2(1− cos θ), (49)

whereE is the energy of the radiated parton andθ the angle it forms with respect to the final-state parton1781

that has emitted it, both taken in the partonic centre-of-mass frame. The scales used in the calculation1782

of the POWHEGB function (i.e. the function that is used to generate the underlying Born variables to1783

which the POWHEG BOX attaches the radiation ones) are instead the ones defined in the forthcoming1784

Eq. (53).1785

6.2 VBF parameters and cuts1786

The numerical results presented in Section 6.3 have been computed using the values of the EW parame-1787

ters given in Appendix??. The electromagnetic coupling is fixed in theGF scheme, to be1788

αGF=

√2GFM

2W(1−M2

W/M2Z)/π = 1/132.4528 . . . . (50)

The weak mixing angle is defined in the on-shell scheme1789

sin2 θw = 1−M2

W

M2Z

= 0.222645 . . . . (51)

We consider the following set of Higgs-boson masses and corresponding total widths1790

MH [GeV] 120 150 200 250 500 600

ΓH [GeV] 0.00348 0.0173 1.43 4.04 68.0 123(52)

The renormalization and factorization scales are set equalto theW-boson mass1791

µR = µF =MW. (53)

In the calculation of the NLO differential cross sections, we have used the MSTW2008 and CTEQ6.61792

parton distribution functions (PDF).1793

Jets are constructed according to the anti-kT algorithm, with the rapidity-azimuthal separation1794

∆R = 0.5, using the default recombination scheme (E scheme). Jets are subject to the following cuts1795

pTj > 20 GeV, |yj| < 4.5 , (54)

whereyj denotes the rapidity of the (massive) jet. Jets are ordered according to theirpT in decreasing1796

progression. The jet with highestpT is called leading jet, the one with next highestpT subleading jet,1797

and both are the tagging jets. Only events with at least two jets are kept. They must satisfy the additional1798

constraints1799

|yj1 − yj2| > 4 , mjj > 600 GeV. (55)

The Higgs boson is generated off shell, according to Eqs. (46) or (48), and there are no cuts applied to1800

its decay products.1801

6.3 Results1802

In the following we present a few results for the LHC at7 TeV calculated with HAWK, VBFNLO and1803

POWHEG, for the Higgs-boson masses listed in Eq. (52).1804

November 18, 2011 – 11 : 26 DRAFT 87

Table 29: Higgs-boson NLO cross sections at7 TeV with VBF cuts and CTEQ6.6 PDF set with and without EWcorrections, relative EW corrections and theoretical uncertainties from PDF and scale variations.

w/ EW corr w/o EW corr EW corr uncert.MH HAWK VBFNLO HAWK VBFNLO HAWK PDF scale

[GeV] [fb] [fb] [fb] [fb] [%] [%] [%]120 261.18± 0.43 256.35± 0.34 283.91± 0.42 283.40± 0.18 −8.0± 0.2 ±3.5 +0.5−0.5150 218.40± 0.36 216.08± 0.45 236.75± 0.35 237.96± 0.20 −7.8± 0.2 ±3.5 +1.0−0.5200 165.22± 0.24 162.79± 0.23 176.46± 0.24 176.96± 0.10 −6.4± 0.2 ±3.6 +0.6−0.6250 123.81± 0.17 120.86± 0.17 133.13± 0.16 133.34± 0.08 −7.0± 0.2 ±3.8 +0.6−0.5500 38.10± 0.07 34.51± 0.06 38.38± 0.07 38.17± 0.02 −0.7± 0.3 ±4.3 +0.4−0.4600 26.34± 0.12 21.94± 0.04 25.70± 0.11 25.37± 0.01 2.5± 0.7 ±4.4 +0.7−0.6

6.3.1 Total cross sections with VBF cuts1805

We have calculated the cross section for VBF at NLO within thecuts given in Section 6.2 using the1806

MSTW2008NLO and CTEQ6.6 PDF sets with and without EW corrections. The results are shown in1807

Tables 29 and 31 including the statistical errors of the Monte Carlo integration. The results of HAWK1808

and VBFNLO without EW corrections agree within roughly 1%. The EW corrections of both codes dis-1809

agree, in particular for large Higgs-boson masses. The EW corrections calculated with HAWK amount omitVBFNLOnumbers!

1810

to −8% for small Higgs-boson masses, decrease and change sign withincreasing Higgs-boson mass1811

and reach +2.4% forMH = 600 GeV. We also show the scale uncertainties obtained with HAWKby1812

varying the factorization and renormalization scales in the rangeMW/2 < µ < 2MW17 and the PDF1813

uncertainties obtained from the corresponding 90% C.L. error PDFs according to the CTEQ prescription1814

with symmetric errors [91]. We give these uncertainties only for the cross section with EW corrections1815

as they are practically the same without EW corrections. Both the PDF uncertainties and the scale uncer-1816

tainties are larger than for the total cross section withoutcuts (c.f. Ref. [6]). Note that we do not include1817

the uncertainties from varyingαs in the PDFs. includeαs?

1818

Tables 30 and 32 show the corresponding results obtained with POWHEG at pure NLO and1819

with PYTHIA or HERWIG parton showers. The NLO results in the second columns can be directly1820

compared with the NLO results without EW corrections of Tables 29 and 31. While POWHEG and1821

HAWK/VBFNLO agree within integration errors for small Higgs-boson masses the results differ by1822

13% and 25% forMH = 500 GeV andMH = 600 GeV. This difference can be traced to the different1823

Breit-Wigner distributions (46) and (48) used in the codes and has to be considered as a theoretical1824

uncertainty due to the treatment of the unstable Higgs boson. Inclusion of the parton showers reduces1825

the cross sections by 5%–7% with a larger effect for small Higgs-boson masses, because more events1826

are cut away after showering. The results for PYTHIA and HERWIG parton showers are in good1827

agreement.1828

6.3.2 Differential distributions1829

In this section we present some results for differential distributions for the setup defined in Section 6.21830

and CTEQ6.6 PDFs. For each distribution we show the NLO results from HAWK with (blue solid)1831

and without (green dash-dotted) EW corrections, the results of VBFNLO with EW corrections (black1832

long-dashed) and the NLO results from POWHEG (red short-dashed). Each plot contains results for1833

MH = 120GeV (upper set of curves) and forMH = 600GeV (lower set of curves). In addition we1834

show the relative EW corrections obtained from HAWK. These could be taken into account in any QCD-1835

based prediction for the respective distributions (based on the cuts of Section 6.2) via reweighting. The1836

17More precisely, we calculated the cross sections for 5 scalecombinations{µR, µF} = {1, 1}, {0.5, 1}, {2, 1}, {1, 0.5},and{1, 2}, and took the maximum and the minimum of the results as upper and lower bound of the variation.

November 18, 2011 – 11 : 26 DRAFT 88

Table 30: POWHEG Higgs-boson cross sections at7 TeV with VBF cuts and CTEQ6.6 PDF set: fixed NLOresults, POWHEG showered by PYTHIA (PY) and by HERWIG (HW).

MH POWHEG NLO POWHEG+ PY POWHEG+ HW[GeV] [fb] [fb] [fb]120 282.87± 0.75 262.96± 0.99 262.04± 0.99150 237.30± 0.57 221.54± 0.79 219.95± 0.79200 177.05± 0.38 164.55± 0.55 163.83± 0.55250 132.93± 0.26 124.19± 0.40 123.65± 0.40500 34.04± 0.07 31.92± 0.09 31.78± 0.10600 20.56± 0.03 19.47± 0.06 19.30± 0.06

Table 31: Higgs-boson NLO cross sections at7 TeV with VBF cuts and MSTW2008NLO PDF set with andwithout EW corrections, relative EW corrections and theoretical uncertainties from PDF and scale variations.

w/ EW corr w/o EW corr EW corr uncert.MH HAWK VBFNLO HAWK VBFNLO HAWK PDF scale

[GeV] [fb] [fb] [fb] [fb] [%] [%] [%]120 259.74± 0.69 254.52± 0.86 282.17± 0.68 281.48± 0.20 −8.0± 0.2 ±5.0 +0.6− 0.5150 217.58± 0.37 214.93± 0.30 235.73± 0.36 236.05± 0.14 −7.7± 0.2 ±5.1 +0.5−0.5200 164.18± 0.24 161.90± 0.24 175.29± 0.23 175.77± 0.10 −6.3± 0.2 ±5.0 +0.5−0.5250 122.73± 0.20 119.07± 0.60 131.90± 0.19 131.75± 0.08 −7.0± 0.2 ±5.2 +0.5−0.7500 37.26± 0.09 33.63± 0.10 37.57± 0.10 37.38± 0.02 −0.8± 0.2 ±5.2 +0.7−0.4600 25.71± 0.08 21.38± 0.04 25.21± 0.08 24.75± 0.01 2.0± 0.2 ±5.1 +0.4−0.7

Table 32: POWHEG Higgs-boson cross sections at7 TeV with VBF cuts and MSTW2008NLO PDF set: fixedNLO results, POWHEG showered by PYTHIA (PY) and by HERWIG (HW).

MH POWHEG NLO POWHEG + PY POWHEG + HW[GeV] [fb] [fb] [fb]120 281.97± 0.76 262.23± 0.99 260.44± 1.00150 235.29± 0.67 218.24± 0.79 216.70± 0.79200 175.38± 0.42 162.80± 0.55 161.45± 0.55250 131.57± 0.26 123.21± 0.40 122.62± 0.40500 33.21± 0.06 31.03± 0.09 30.85± 0.09600 20.03± 0.03 18.74± 0.05 18.67± 0.06

data files of the histograms are provided at the wiki page of the VBF working group18.1837

Figure 38 displays the rapidityyH and the transverse momentumpTH of the Higgs-boson. While1838

the difference in normalization between POWHEG and HAWK forthe high Higgs-boson mass has1839

been explained for the total cross section, the shapes of thedistributions agree well between the different1840

codes. While EW corrections are flat for the rapidity distribution, the EW corrections increase with1841

increasingpTH.1842

For the distributions in the transverse momentum of the leading and subleading jets,pTj1 and1843

pTj2, shown in Figure 39 and of the di-jet invariant massmjj, presented on the left-hand side of Fig-1844

ure 40 similar remarks are applicable. The shapes of the different distributions agree well between the1845

18https://twiki.cern.ch/twiki/bin/view/LHCPhysics/VBF

November 18, 2011 – 11 : 26 DRAFT 89

Hy

-3 -2 -1 0 1 2 3

/dy

[fb]

σd

0

20

40

60

80

100

LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

Hy

-3 -2 -1 0 1 2 3

[%]

EW

δ

-10

-5

0

5

= 120 GeVHM

= 600 GeVHM

[GeV]TH

p0 50 100 150 200 250 300 350 400 450 500

[fb/

GeV

]T

/dp

σd

-310

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

[GeV]TH

p0 50 100 150 200 250 300 350 400 450 500

[%]

EW

δ

-30

-20

-10

0

= 120 GeVHM

= 600 GeVHM

Fig. 38: Higgs-boson rapidity (left) and transverse momentum (right). The top plots show the comparison betweenHAWK (with and without EW corrections), POWHEG at NLO and VBFNLO for MH = 120 GeV (upper setof curves) andMH = 600 GeV (lower set of curves) for MSTW2008NLO PDF set. The bottomplots display thepercentage EW corrections, for each of the two mass points.

[GeV]Tj1

p50 100 150 200 250 300 350

[fb/

GeV

]T

/dp

σd

-210

-110

1

LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

[GeV]Tj1

p50 100 150 200 250 300 350

[%]

EW

δ

-20

-10

0

= 120 GeVHM

= 600 GeVHM

[GeV]Tj2

p20 40 60 80 100 120 140

[fb/

GeV

]T

/dp

σd

-110

1

10

LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

[GeV]Tj2

p20 40 60 80 100 120 140

[%]

EW

δ

-20

-10

0

= 120 GeVHM

= 600 GeVHM

Fig. 39: Transverse momentum of the leading (left) and sub-leading jet (right). The top plots show the comparisonbetween HAWK (with and without EW corrections), POWHEG at NLO and VBFNLO forMH = 120 GeV(upper set of curves) andMH = 600 GeV (lower set of curves) for MSTW2008NLO PDF set. The bottomplotsdisplay the percentage EW corrections, for each of the two mass points.

different codes. The EW corrections reduce the cross section more and more with increasing energy1846

scale, a generic behaviour of EW corrections that can be attributed to weak Sudakov logarithms. EW1847

corrections range from a few to−20%. The distribution in the azimuthal-angle separation between the1848

two tagging jetsφjj is shown on the right-hand side of Figure 40. In particular for the light Higgs boson,1849

the electroweak corrections distort the distribution at the level of several per cent.1850

November 18, 2011 – 11 : 26 DRAFT 90

[GeV]jjm1000 1500 2000 2500 3000

[fb/

GeV

]jj

/dm

σd

-210

-110 LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

[GeV]jjm1000 1500 2000 2500 3000

[%]

EW

δ

-10

0

= 120 GeVHM

= 600 GeVHM

jjϕ∆

0 0.5 1 1.5 2 2.5 3

[fb]

jjϕ∆

/dσd

1

10

210

310

LH

C H

IGG

S X

S W

G 2

011

HAWK w/ EW Corr

POWHEG

HAWK w/o EW Corr

VBFNLO w/ EW Corr

jjϕ∆

0 0.5 1 1.5 2 2.5 3

[%]

EW

δ

-0.2

0

0.2

= 120 GeVHM

= 600 GeVHM

Fig. 40: Di-jet invariant mass (left) and azimuthal separation between the two tagging jets (right). The top plotsshow the comparison between HAWK (with and without EW corrections), POWHEG and VBFNLO forMH =

120 GeV (upper set of curves) andMH = 600 GeV (lower set of curves) for MSTW2008NLO PDF set. Thebottom plots display the percentage EW corrections for eachof the two mass points.

[GeV]jjm600 800 1000 1200 1400 1600 1800 2000 2200 2400

[fb/

GeV

]jj

/dm

σd

0

0.1

0.2

0.3

0.4

0.5

LH

C H

IGG

S X

S W

G 2

011

POWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

|j2

-yj1

|y4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9

| [fb

]j2

-yj1

/d|y

σd

0

20

40

60

80

100

120

LH

C H

IGG

S X

S W

G 2

011

POWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

Fig. 41: Invariant mass of the two tagging jets,mjj , (left) and absolute value of the distance in rapidity of thetwotagging jets,|yj1 − yj2 |, (right). The solid blue line is the NLO result, while the green and the red curves representthe results of POWHEG interfaced to HERWIG and PYTHIA, respectively.

6.3.3 POWHEGdifferential distributions1851

In this section, we present a few results obtained by POWHEG interfaced to HERWIG and PYTHIA,1852

in the configuration described in Section 6.2 and for a Higgs-boson mass of120 GeV. These results1853

have been generated using the MSTW2008 pdf set. They depend only very slightly on the value of the1854

Higgs-boson mass and on the PDF set used, so similar conclusions can be drawn using NNPDF2.0 and1855

CTEQ6.6. We have generated 0.5M events with the POWHEG BOX. We have run PYTHIA with the1856

Perugia 0 tuning and HERWIG in its default configuration, with intrinsicpT -spreading of 2.5 GeV.1857

In Figure 41 we plot the invariant mass of the two tagging jets, mjj, and the absolute value of1858

the distance in rapidity of the two tagging jets,|yj1 − yj2|. In all distributions presented in this section1859

the solid blue lines represent the NLO result, and the green and the red curves the results of POWHEG1860

interfaced to HERWIG and PYTHIA, respectively. The effect of the cuts on the showered results1861

produces a reduction of the total cross section that appearsmanifest in the two distributions shown.1862

There is an agreement between the two showered results, slightly below the NLO curves. This behaviour1863

November 18, 2011 – 11 : 26 DRAFT 91

j3y

-4 -3 -2 -1 0 1 2 3 4

[fb]

j3/d

yσd

0

2

4

6

8

10

LH

C H

IGG

S X

S W

G 2

011

POWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

njets1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

(nje

ts)

[fb]

σ

-210

-110

1

10

210

LH

C H

IGG

S X

S W

G 2

011

POWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

Fig. 42: Rapidity distribution of the third hardest jet,yj3 (left) and exclusive jet-multiplicity (right). The solidblue line is the NLO result, while the green and the red curvesrepresent the results of POWHEG interfaced toHERWIG and PYTHIA respectively.

is general for several physical distributions.1864

Larger disagreements between the NLO and showered results and between the two showering1865

programs can be seen in Figure 42. On the left-hand side of this figure, we have plotted the rapidity1866

distribution of the third hardest jet (the one with highestpT after the two tagging jets). The distributions1867

obtained using POWHEG interfaced to HERWIG and PYTHIA, are very similar but show that fewer1868

events pass the cuts with respect to the unshowered NLO result. Nevertheless, they confirm the behaviour1869

that the third jet tends to be emitted in the vicinity of either of the tagging jets. We recall here that, strictly1870

speaking, this is a LO distribution, since the third jet in the NLO calculation comes only from the real-1871

emission contributions.1872

We turn now to quantities that are more sensitive to the collinear and soft physics of the shower.1873

The jet activity is one of such quantity. In order to quantifyit, we plot the exclusive jet-multiplicity1874

distribution for jets that pass the cuts of Eq. (54) in the right-hand plot of Figure 42. The first two tagging1875

jets and the third jet are well represented by the NLO cross section, that obviously cannot contribute to1876

events with more than three jets. From the 4th jet on, the showers of HERWIG and PYTHIA produce1877

sizable differences (note the log scale of the plot), the jets from PYTHIA being harder and/or central1878

than those from the HERWIG shower.1879

Striking differences between the NLO results and POWHEG canbe seen in the relative transverse1880

momentum of all the particles clustered inside one of the twotagging jetsprel,jT . This quantity brings1881

information on the “shape” of the jet. It is defined as follows:1882

- for each jet we perform a longitudinal boost to a frame wherethe jet has zero rapidity.1883

- In this frame, we compute the quantity1884

prel,jT =∑

i∈j

|~ki × ~p j||~p j| , (56)

whereki are the momenta of the particles that belong to the jet with momentumpj.1885

This quantity is thus the sum of the absolute values of the transverse momenta, taken with respect to the1886

jet axis, of the particles inside the jet, in the frame specified above. In the left-hand-side of Figure 431887

we have plotted the relative transverse momentum with respect to the first tagging jet,prel,j1T . While the1888

black NLO curve is diverging asprel,j1T approaches zero, the Sudakov form factors damp this region in1889

the POWHEG results.1890

November 18, 2011 – 11 : 26 DRAFT 92

[GeV]rel, j1

Tp

0 5 10 15 20 25 30

[fb/

GeV

]re

l, j1

T/d

pσd

-110

1

10 LH

C H

IGG

S X

S W

G 2

011

POWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

[GeV]T,veto

p20 22 24 26 28 30 32 34 36 38 40

veto

p

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

LH

C H

IGG

S X

S W

G 2

011

W=MF

µ=R

µPOWHEG NLO

W=2MF

µ=R

µPOWHEG NLO

/2W=MF

µ=R

µPOWHEG NLO

POWHEG + PYTHIA

POWHEG + HERWIG

Fig. 43: Relative transverse momentumprel,j1T of all the particles clustered inside the first tagging jet, in thereference frame where the jet has zero rapidity, defined according to Eq. (56) (left) and probability of finding aveto jet defined as in Eq. (58) as a function ofpT,veto (right). The solid blue line is the NLO result, while the greenand the red curves represent the results of POWHEG interfaced to HERWIG and PYTHIA respectively. TheNLO blue curve is computed withµR = µF = MW, while the NLO results obtained withµR = µF =MW/2 andµR = µF = 2MW are shown as dashed and dash-dotted lines (upper and lower respectively).

As last comparison, we have studied the probability of finding veto jets, i.e. jets that fall within1891

the rapidity interval of the two tagging jets1892

min (yj1, yj2) < yj < max (yj1 , yj2) . (57)

In fact, for the central-jet-veto proposal, events are discarded if any additional jet with a transverse1893

momentum above a minimal value,pT,veto, is found between the tagging jets. The probability,Pveto, of1894

finding a veto jet is defined as1895

Pveto =1

σNLO2

∫ ∞

pT,veto

dp j,vetoT

dσ

dp j,vetoT

, (58)

wherep j,vetoT is the transverse momentum of the hardest veto jet, andσNLO

2 is the total cross section1896

(within VBF cuts) forHjj production at NLO. In the right-hand plot of Figure 43 we haveplotted the1897

NLO and POWHEG interfaced to HERWIG and PYTHIA predictions.ForMH = 120 GeV, we have1898

σNLO2 = 282 fb, with the settings described in Section 6.2. In addition to the NLO curve obtained with1899

µR = µF =MW, we have added the NLO results computed withµR = µF =MW/2 (upper dashed line)1900

andµR = µF = 2MW (lower dash-dotted line) that show that the POWHEG curves are consistent with1901

the LO band obtained with a change of the renormalization andfactorization scale by a factor of two1902

and that the distance between POWHEG+PYTHIA and POWHEG+HERWIG is comparable with the1903

scale uncertainty of the LO result.1904

6.3.4 Efficiency of VBF cuts1905

Finally we study the selection efficiency of VBF cuts and the cross section within VBF cuts at NLO-QCD1906

as a function of a jet veto.1907

In Figure 44, we plot the total efficiency of all selection cuts (on the left) and the cross-section after1908

cuts (on the right) at NLO QCD level. In all the plots, the red and blue curves show the results obtained1909

by varying the factorization and renormalization scales byfactors of two. The NLO cross-sections and1910

efficiencies after a jet veto cut of 20 GeV are shown together with their scale and PDF uncertainties in1911

Table 33.1912

November 18, 2011 – 11 : 26 DRAFT 93

[GeV]T, veto

p20 30 40 50 60 70 80 90 100

Sel

ectio

n E

ffici

ency

0.195

0.2

0.205

0.21

0.215

Central Value

renµ 2→

renµ,

facµ 2→

facµ

/2ren

µ →ren

µ/2, fac

µ →fac

µ

/2ren

µ →ren

µ, fac

µ 2→fac

µ

renµ 2→

renµ/2,

facµ →

facµ

[GeV]T, veto

p20 30 40 50 60 70 80 90 100

Cro

ss-s

ectio

n af

ter

veto

[fb]

255

260

265

270

275

280

285

Central Value

renµ 2→

renµ,

facµ 2→

facµ

/2ren

µ →ren

µ/2, fac

µ →fac

µ/2

renµ →

renµ,

facµ 2→

facµ

renµ 2→

renµ/2,

facµ →

facµ

Fig. 44: Efficiency of the forward jet tagging and central-jet-veto cuts as a function ofpT,veto (left) and cross-section after all cuts as a function ofpT,veto (right).

Table 33: Cross-sections and efficiencies from VBFNLO for the full VBFselection including the jet veto, and thecorresponding uncertainties from the QCD scale and parton density functions.

Cross-section EfficiencyMH Central PDF scale Central PDF scale

[GeV] [fb] [%] [%] [%] [%] [%]120 263.61 ±10.64 ±12.74 0.201 ± 0.008 ±0.0031150 219.83 ±7.54 ±10.94 0.221 ± 0.007 ±0.0035200 164.24 ±6.59 ±7.37 0.253 ± 0.010 ±0.0038250 123.68 ±4.67 ±6.43 0.280 ± 0.011 ±0.0038500 33.74 ±1.49 ±1.81 0.366 ± 0.018 ±0.0036600 21.00 ±0.93 ±1.11 0.386 ± 0.019 ±0.0030

November 18, 2011 – 11 : 26 DRAFT 94

7 WH/ZH production mode191913

7.1 Theoretical developments1914

In the previous report [6] state-of-the-art predictions and error estimates for the total cross sections for1915

pp → WH/ZH have been compiled, based on (approximate) next-to-next-to-leading-order (NNLO)1916

QCD and next-to-leading-order (NLO) electroweak (EW) corrections. In more detail, the QCD correc-1917

tions (∼ 30%) comprise Drell–Yan-like contributions [201], which respect factorization according to1918

pp → V∗ → VH and represent the dominant parts, and a smaller remainder, which contributes beyond1919

NLO. The NLO EW corrections to the total cross sections were evaluated as in Ref. [202] and turn out to1920

be about−(5−10)%. In the report [6] the Drell–Yan-like NNLO QCD predictions are dressed with the1921

NLO EW corrections in fully factorized form as suggested in Ref. [203], i.e. the EW corrections simply1922

enter as multiplicative correction factor, which is ratherinsensitive to QCD scale and parton distribu-1923

tion function (PDF) uncertainties. For the LHC with a centre-of-mass (CM) energy of7(14) TeV the1924

QCD scale uncertainties were assessed to be about1% and1−2(3−4)% for WH andZH production,1925

respectively, while uncertainties of the PDFs turn out to beabout3−4%.1926

After the completion of the report [6] theoretical progresshas been made in various directions:1927

– On the QCD side, the Drell–Yan-like NNLO corrections toWH production are available now [204]1928

including the full kinematical information of the process and leptonic W decays.1929

– For total cross sections the non-Drell–Yan-like remainder at NNLO QCD has been calculated1930

recently [205]; in particular, this includes contributions with a top-quark induced gluon–Higgs1931

coupling. As previously assumed, these effects are at the percent level. They typically increase1932

towards larger Higgs masses and scattering energies, reaching about2.5%(3%) for ZH production1933

at 7 TeV(14 TeV). Since these Yukawa-induced terms arise for the first time atO(α2s ), they also1934

increase the perturbative uncertainty which, however, still remains below the error from the PDFs.1935

– On the EW side, the NLO corrections have been generalized tothe more complex processes1936

pp → WH → νllH and pp → ZH → l−l+H/νlνlH including the W/Z decays, also fully1937

supporting differential observables [?]; these results are available as part of the HAWK Monte1938

Carlo program [194], which was originally designed for the description of Higgs production via1939

vector-boson fusion including NLO QCD and EW corrections [192].1940

The following numerical results on differential quantities are, thus, obtained as follows:1941

– WH production: The fully differential (Drell–Yan-like) NNLO QCD prediction of Ref. [204] is1942

reweighted with the relative EW correction factor calculated with HAWK, analogously to the1943

previously used procedure for the total cross section. The reweighting is done bin by bin for each1944

distribution.1945

– ZH production: Here the complete prediction is obtained with HAWK including NLO QCD and1946

EW corrections, employing the factorization of relative EWcorrections as well.1947

7.2 Numerical results1948

For the numerical results in this section, we have used the following setup. The renormalization and1949

factorization scales have been identified and set to1950

µR = µF =MH +MV, (59)

whereMV is theW/Z-boson mass for WH/ZH production. We have employed the MRST2008 PDF sets,1951

using the corresponding central LO, NLO, and NNLO sets at thegiven order in QCD. The relative EW1952

19S. Dittmaier, R.V. Harlander, J. Olsen, G. Piacquadio (eds.); A. Denner, G. Ferrera, M. Grazzini, S. Kallweit, A. Mück,F. Tramontano.

November 18, 2011 – 11 : 26 DRAFT 95

corrections have been calculated using the NLO sets, but hardly depend on the PDF and scale choice.1953

We use theGF scheme to fix the electromagnetic couplingα and use the values ofαs associated to the1954

given PDF set. For the QCD predictions toWH production, we employ the full CKM matrix which1955

enters via global factors multiplying the different partonic channels. For all the HAWK predictions, we1956

neglect mixing of the first two generations with the third generation. In the EW loop corrections, the1957

CKM matrix is set to unity, since quark mixing is negligible there. ForZH production, bottom quarks1958

in the initial state are only included in LO within HAWK because of their small impact on the cross1959

sections.1960

Both the NNLO QCD prediction as well as the HAWK predictions are obtained for off-shell1961

vector bosons. The vector-boson width can be viewed as a freeparameter of the calculation, and we1962

have chosenΓW = 2.141 GeV andΓZ from the default input. The NNLO QCD calculation [204]1963

predicts the integratedW-boson production cross section in the presence of the cuts defined below, so1964

that it had to be multiplied by the branching ratioBRW→lν for a specific leptonic final state. Because1965

the EW radiative corrections to the BR are included in the EW corrections from HAWK, the partial1966

W width has to be used at Born level in the QCD-improved cross section, i.e.BRW→lν = ΓBornW→lν/ΓW,1967

whereΓBornW→lν = GFM

3W/(6

√2π). Using any different input value forΓnew

W , all results are thus, up to1968

negligible corrections, changed by the ratioΓW/ΓnewW . In the HAWK prediction, the branching ratios for1969

the different leptonic channels are implicitly included bycalculating the full matrix elements. However,1970

up to negligible corrections the same scaling holds if another numerical value for the input width was1971

used. In particular, the relative EW corrections hardly depend onΓW.1972

All results are given for a specific leptonic decay mode, e.g.for He+e− orHµ+µ− production, and1973

are not summed over lepton generations. While for charged leptons the results depend on the prescription1974

for lepton–photon recombination (see below), the results for invisibleZ decays, of course, do not depend1975

on the neutrino flavour and can be trivially obtained by multiplying theHνlνl results by three.1976

In the calculation of EW corrections, we alternatively apply two versions of handling photons that1977

become collinear to outgoing charged leptons. The first option is to assume perfect isolation between1978

charged leptons and photons, an assumption that is at least approximately fulfilled for (bare) muons.1979

The second option performs a recombination of photons and nearly collinear charged leptons and, thus,1980

mimics the inclusive treatment of electrons within electromagnetic showers in the detector. Specifically,1981

a photonγ and a leptonl are recombined forRlγ < 0.1, whereRlγ =√

(yl − yγ)2 + φ2lγ is the usual1982

separation variable in they−φ-plane withy denoting the rapidity andφlγ the angle betweenl andγ in1983

the plane perpendicular to the beams. Ifl andγ are recombined, we simply add their four-momenta1984

and treat the resulting object as quasi-lepton. If more thanone charged lepton is present in the final1985

state, the possible recombination is performed with the lepton delivering the smaller value ofRlγ . The1986

corresponding EW corrections are labeledδbare andδrec, respectively.1987

After employing the recombination procedure we apply the following cuts on the charged leptons,1988

pT,l > 20 GeV, |yl| < 2.5, (60)

wherepT,l is the transverse momentum of the leptonl. For channels with at least one neutrino in the1989

final state we require a missing transverse momentum1990

pT,miss > 25 GeV, (61)

which is defined as the total transverse momentum of the neutrinos in the event. In addition, we apply1991

the cuts1992

pT,H > 200 GeV, pT,W/Z > 190 GeV (62)

on the transverse momentum of the Higgs and the weak gauge bosons, respectively. The corresponding1993

selection of events with boosted Higgs bosons is improving the signal-to-background ratio in the context1994

November 18, 2011 – 11 : 26 DRAFT 96

of employing the measurement of the jet substructure inH → bb decays leading to a single fat jet.1995

The need for background suppression calls for (almost) identical cuts on the transverse momentum of1996

the vector bosons and the Higgs boson. However, symmetric cuts induce large radiative corrections in1997

fixed-order calculations in the correspondingpT distributions near the cut. Since the Higgs boson and1998

the vector boson are back-to-back at LO, any initial-state radiation will either decreasepT,H or pT,W/Z1999

and the event may not pass the cut anymore. Hence, the differential cross section near the cut is sensitive2000

to almost collinear and/or rather soft initial-state radiation. By choosing the above (slightly asymmetric)2001

cuts this large sensitivity to higher-order corrections can be removed for the importantpT,H-distribution.2002

Of course, since the LO distribution forpT,W/Z is vanishing forpT,W/Z < 200 GeV due to thepT,H cut,2003

the higher-order corrections to thepT,W/Z distributions are still large in this region.2004

In the following plots, we show several relative corrections and the absolute cross-section predic-2005

tions based on factorization for QCD and EW corrections,2006

σ = σQCD × (1 + δrecEW) + σγ , (63)

whereσQCD is the best QCD prediction at hand,δrecEW is the relative EW correction with recombination2007

andσγ is the cross section due to photon-induced processes which are at the level of1% and estimated2008

employing the MRSTQED2004 PDF set for the photon. In detail,we discuss the distributions inpT,H,2009

pT,V, pT,l, andyH. More detailed results can be found in Ref. [?].2010

Figure 45 shows the distributions for the two WH production channelsHl+ν andHl−ν and for the2011

ZH production channelsHl+l− andHνν. The respective EW corrections are depicted in Figure 46 forthe2012

two different treatments of radiated photons, but the difference between the two versions, which amounts2013

to 1−3%, is small. The bulk of the EW corrections, which are typically in the range of−(10−15)%, is2014

thus of pure weak origin. In allpT distributions the EW corrections show a tendency to grow more and2015

more negative for largerpT, signalling the onset of the typical logarithmic high-energy behaviour (weak2016

Sudakov logarithms). The rapidity distributions receive rather flat EW corrections, which resemble the2017

ones to the respective integrated cross sections. Note thatthe latter are significantly larger in size than2018

the ones quoted in Ref. [6] for the total cross sections, mainly due to the influence of thepT cuts on2019

the Higgs and gauge bosons, which enforce the dominance of larger scales in the process. This can be2020

clearly seen upon comparing the results with the ones shown in Figure 47, where only the basic cuts are2021

applied, but not (7.2). For the basic cuts, the EW corrections are globally smaller in size by about5%,2022

but otherwise show the same qualitative features.2023

The relative EW corrections shown here could be taken into account in any QCD-based prediction2024

for the respective distributions (based on the quoted cuts)via reweighting. For this purpose the data2025

files of the histograms are available at the wiki page of the WH/ZH working group20. The small photon-2026

induced contributions, which are included in our best prediction and at the level of1% for WH production2027

and negligible for ZH production, are also available and could be simply added.2028

For definiteness, in Table 34, we show the integrated resultscorresponding to the cuts in the2029

boosted setup.2030

20https://twiki.cern.ch/twiki/bin/view/LHCPhysics/WHZH

November 18, 2011 – 11 : 26 DRAFT 97

H l−ν

H l+ν

pT,H[GeV]

dσ/dpT,H[fb/GeV]

300280260240220200

0.025

0.02

0.015

0.01

0.005

0

LHC

HiggsXS

WG

2011

H νν

H l+l−

pT,H[GeV]

dσ/dpT,H[fb/GeV]

300280260240220200

0.025

0.02

0.015

0.01

0.005

0

LHC

HiggsXS

WG

2011

H l−ν

H l+ν

pT,V[GeV]

dσ/dpT,V[fb/GeV]

300280260240220200

0.02

0.015

0.01

0.005

0

LHC

HiggsXS

WG

2011

H νν

H l+l−

pT,V[GeV]

dσ/dpT,V[fb/GeV]

300280260240220200

0.02

0.015

0.01

0.005

0

LHC

HiggsXS

WG

2011

H l−ν

H l+ν

pT,l±[GeV]

dσ/dpT,l±[fb/GeV]

30025020015010050

0.01

0.008

0.006

0.004

0.002

0

LHC

HiggsXS

WG

2011

H l+l−

pT,l+[GeV]

dσ/dpT,l+[fb/GeV]

30025020015010050

0.01

0.008

0.006

0.004

0.002

0LHC

HiggsXS

WG

2011

H l−ν

H l+ν

yH

dσ/dyH[fb]

210−1−2

0.6

0.5

0.4

0.3

0.2

0.1

0

LHC

HiggsXS

WG

2011

H νν

H l+l−

yH

dσ/dyH[fb]

210−1−2

0.6

0.5

0.4

0.3

0.2

0.1

0

LHC

HiggsXS

WG

2011

Fig. 45: Predictions for thepT,H, pT,V, pT,l, andyH distributions (top to bottom) for Higgs strahlung offWbosons (left) andZ bosons (right) for boosted Higgs bosons at the7 TeV LHC forMH = 120 GeV.

November 18, 2011 – 11 : 26 DRAFT 98

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,H[GeV]

δEW[%]

300280260240220200

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

pT,H[GeV]

δEW[%]

300280260240220200

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,V[GeV]

δEW[%]

300280260240220200

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

pT,V[GeV]

δEW[%]

300280260240220200

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,l±[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

−25

LHC

HiggsXS

WG

2011

δbareH l+l−

δrecH l+l−

pT,l+[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

−25LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

yH

δEW[%]

210−1−2

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

yH

δEW[%]

210−1−2

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

Fig. 46: Relative EW corrections for thepT,H, pT,V, pT,l, andyH distributions (top to bottom) for Higgs strahlungoff W bosons (left) andZ bosons (right) for boosted Higgs bosons at the7 TeV LHC forMH = 120 GeV.

November 18, 2011 – 11 : 26 DRAFT 99

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,H[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

pT,H[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,V[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

pT,V[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

pT,l±[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

−25

LHC

HiggsXS

WG

2011

δbareH l+l−

δrecH l+l−

pT,l+[GeV]

δEW[%]

30025020015010050

0

−5

−10

−15

−20

−25LHC

HiggsXS

WG

2011

δbareH l−ν

δrecH l−ν

δbareH l+ν

δrecH l+ν

yH

δEW[%]

210−1−2

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

δH νν

δbareH l+l−

δrecH l+l−

yH

δEW[%]

210−1−2

0

−5

−10

−15

−20

LHC

HiggsXS

WG

2011

Fig. 47: Relative EW corrections for thepT,H, pT,V, pT,l, andyH distributions (top to bottom) for Higgs strahlungoff W bosons (left) andZ bosons (right) for the basic cuts at the7 TeV LHC forMH = 120 GeV.

November 18, 2011 – 11 : 26 DRAFT 100

channel Hl+νl +X Hl−νl +X Hl+l− +X Hνlνl +X

σ/ fb 1.4165(2) 0.62476(7) 0.35178(2) 0.76115(4)

δbareW /% −14.3 −14.0 −11.0 −6.9

δrecW /% −13.3 −13.1 −9.0 −6.9

σγ/ fb 0.0198 0.0096 0.0002 0.0000

Table 34: Integrated cross sections and EW corrections for the different Higgs-strahlung channels in the boostedsetup for the LHC at7 TeV forMH = 120 GeV.

November 18, 2011 – 11 : 26 DRAFT 101

8 ttH Process212031

The process of Higgs radiation off top quarksqq/gg → Htt becomes particularly relevant for Higgs2032

searches at the LHC in the light Higgs mass region below∼ 130 GeV. Given the recent Higgs-boson2033

exclusion limits provided by the Tevatron and LHC experiments, and given the indirect constraints pro-2034

vided by the electroweak precision fits [206], the ligh-Higgs-boson mass region will play a crucial role2035

in confirming or excluding the Higgs mechanism of electroweak symmetry breaking as minimally im-2036

plemented in the Standard Model. Indeed, it will be hard for the LHC running at√s = 7 TeVto exclude2037

the light-Higgs-boson mass region with enough statisticalsignificance and more in depth studies will be2038

necessary in order to extract more information from the available data. In this context, a careful study of2039

ttH production will become very important. Finally, if a light scalar is discovered, the measurement of2040

thettH production rate can provide relevant information on the top–Higgs Yukawa coupling.2041

The full next-to-leading-order (NLO) QCD corrections tottH production have been calculated2042

[207–210] resulting in a moderate increase of the total cross section at the LHC by at most∼ 20%,2043

depending on the value ofMH and on the PDF set used. More importantly, the QCD NLO corrections2044

reduce the residual scale dependence of the inclusive crosssection fromO(50%) to a level ofO(10%),2045

when the renormalization and factorization scales are varied by a factor of 2 above and below a conven-2046

tional central scale choice (the NLO studies in the literature useµ0 = mt +MH/2), and clearly show2047

their importance in obtaining a more stable and reliable theoretical prediction.2048

Using the NLO codes developed by the Authors of [207–210], ina previous report [6] we studied2049

the inclusivettH production at both√s = 7 and 14 TeVand we provided a breakdown of the estimated2050

theoretical error from renormalization- and factorization-scale dependence, fromαs, and from the choice2051

of Parton Distribution Functions (PDFs). The total theoretical errors were also estimated combining the2052

uncertainties from scale dependence,αs dependence, and PDF dependence according to the recommen-2053

dation of the LHC Higgs Cross Section Working Group [6]. For low Higgs-boson masses, the theoretical2054

errors typically amount to 10-15% of the corresponding cross sections.2055

In this second report we move towards exclusive studies and address the problem of evaluating2056

the impact of QCD corrections and the corresponding residual theoretical uncertainty in the presence2057

of kinematic constraints and selection cuts that realistically model the experimental measurement. We2058

focus on three main studies: 1) a study of the theoretical uncertainty from scale-dependence,αs, and2059

PDFs on the most significant differential distributions forthe on-shell parton-level processpp → ttH2060

calculated at NLO in QCD (see Sec. 8.1); 2) a study of the effects of interfacing the NLO parton-level2061

calculations with parton-shower Monte Carlo programs, namely PYTHIA and HERWIG, including a2062

comparison between the MC@NLO and POWHEG BOX frameworks, recently applied to the case of2063

ttH production in [211] and [212] respectively (see Sec. 8.2); 3) a study of the the background process2064

pp → ttbb based on the NLO QCD results presented in [213–217], including a comparison between2065

signal and background (pp → ttbb) at the parton level, based on the study presented in [217] (see2066

Sec. 8.3).2067

8.1 NLO distributions for ttH associated production2068

In this section we study the theoretical error on NLO QCD distributions forttH on-shell production at2069

a center of mass energy of 7 TeV(14 TeV?). Input parameters are chosen following the Higgs Cross2070

Section Working Group recommendation [6]. We will considerdistributions in transverse momentum2071

(pT ), pseudorapidity (η), and in theR(t, t), R(t,H), R(t, H), andR(H, tt) variables, whereR is the2072

distance in the(φ, η) plane.2073

We focus on the case of a Higgs boson withMH = 120 GeVand study the dependence of the2074

21C. Collins-Tooth, C. Neu, C. Potter, L. Reina, M. Spira (eds.); G. Bevilacqua, A. Bredenstein, M. Czakon, S. Dawson,A. Denner, S. Dittmaier, R. Frederix, S. Frixione, M. V. Garzelli, V. Hirschi, S. Hoeche, A. Kardos, M. Krämer, F. Krauss,F. Maltoni, C. G. Papadopoulos, R. Pittau, S. Pozzorini, S. Schumann, P. Torrielli, Z. Trócsányi, D. Wackeroth, M. Worek, ....

November 18, 2011 – 11 : 26 DRAFT 102

differential cross sections listed above from the renormalization and factorization scale, fromαs, and2075

from the choice of PDFs. We vary the renormalization and factorization scales together by a factor of 22076

around a central valueµ0 = µR = µF = mt +MH/2. We consider the CTEQ6.6 [218] , MSTW08 [95,2077

101], and NNPDF2.0 [85] sets of PDFs and estimate the error from PDFs andαs according to the2078

PFD4LHC prescription (see [6]).2079

PLOTS and COMMENTS.2080

8.2 Interface of NLO ttH calculation with parton-shower Monte Carlo programs2081

Recently independent NLO QCD calculations ofttH (obtained using the MadLoop [219] and HELAC-2082

NLO [220] packages) have been interfaced with parton showerMonte Carlo programs, namely PYTHIA2083

and HERWIG, using both the MC@NLO [211] and the POWHEG [212] methods22. In the process, the2084

on-shell decays of the final state top/antitop and of the Higgs boson have been included. This represents2085

a crucial improvement in matching the accuracy of NLO QCD calculation to experimental analyses that2086

typically work with the decay products of the originalttH state and impose specific selection cuts on2087

these final state products.2088

These packages are the state-of-the-art tools available for LHC analyses and it is therefore impor-2089

tant to validate them and compare their results. Both the Madloop and HELAC-NLO results have already2090

been validated against the original NLO QCD calculations [207–210], as discussed in [211] and [212]2091

respectively. In this report we compare the predictions of the interface with PYTHIA and HERWIG as2092

realized within the aMC@NLO framework [211] and within the POWHEG BOX framework [212] .2093

We consider the the following set of distributions: ....2094

PLOTS and COMMENTS2095

We limit the comparison to the case ofMH = 120 GeVand to the following choice of parameters2096

...2097

8.3 Thepp → ttbb background2098

In the low Higgs-boson mass region, where a SM Higgs boson mainly decays tobb, QCD ttbb pro-2099

duction represents the most important background. Recently the NLO QCD corrections to thettbb2100

production background have been calculated [213–217]. By choosingµ2R = µ2F = mt√pTbpTb as2101

the central renormalization and factorization scales the NLO corrections increase the background cross2102

section within the signal region by about 20–30%. The scale dependence is significantly reduced to2103

a level significantly below30%. The new predictions for the NLO QCD cross sections with the new2104

scale choiceµ2R = µ2F = mt√pTbpTb are larger than the old LO predictions with the old scale choice2105

µR = µF = mt+mbb/2 by more than100% within the typical experimental cuts [215]. In addition the2106

signal processpp → ttH → ttbb has been added to these background calculations in the narrow-width2107

approximation [217].2108

SHOW PLOTS FROM Binoth et al. (can we have then for 7 Tev?)2109

This makes it possible to study the signal and background processes including the final-state Higgs2110

decay intobb with cuts at the same time at NLO. However, it should be noted that the final-state top2111

decays have not been included at NLO so that a full NLO signal and background analysis including2112

all experimental cuts is not possible so far. The top-quark decays are expected to affect the final-state2113

distributions more than the Higgs decays intobb pairs. The next natural step will then be to interface2114

the NLO calculation ofttbb with PYTHIA and HERWIG. This will provide the ultimate tool to study2115

both signal and background in the presence of both decays of the Higgs-boson and of the top/antitop pair,2116

22More specifically, results in [211] are based on NLO results obtained using the MadLoop package while results in [212]are based on NLO results obtained using the HELAC-NLO package.

November 18, 2011 – 11 : 26 DRAFT 103

For highly boosted Higgs bosons the shapes of the backgrounddistributions are affected by the2117

QCD corrections which thus have to be taken into account properly. The effects of a jet veto for the2118

boosted-Higgs regime require further detailed investigations. A study along these lines has been pre-2119

sented by Bevilacqua et al. (in arXiv:0907.4723) for√s = 14 TeV.2120

PLOTS FROM THIS PAPER WILL BE FINE, BUT MAYBE WE CAN GET PLOTS for 7 TeV?2121

More distributions?2122

November 18, 2011 – 11 : 26 DRAFT 104

9 γγ production mode 232123

9.1 Introduction2124

9.2 Sets of Acceptance Criteria used2125

For the moment this will be ATLAS and CMS ptγ andηγ cuts, plus 1-2 additional possible sets2126

9.3 Signal and background modelling2127

9.3.1 Differential k-factors for gluon-fusion signal2128

9.3.2 Gluon-fusion signal and background interference2129

Include sources of theoretical uncertainty.2130

9.3.3 Differential k-factors for background2131

9.3.4 Review of background-determination methods2132

9.3.5 Isolation criteria for background measurement2133

Joint work with that being done for LH2011. Include relationbetween partonic and particle-level isola-2134

tions.2135

9.4 Uncertainties2136

9.4.1 Impact of joint correlated systematic uncertainty related to the background model used2137

Caveat on how to take into account ’false peak’ from same background model used by ATLAS and CMS.2138

9.4.2 Joint conventions for systematic error calculations2139

For signal k-factors and background determination techniques2140

9.4.3 Realistic 0-jet scale uncertainties via the ’BNL accord’2141

Propagate the uncertainty onσ0 = σtotal − σ≥I relative toσtotal. Check if being done centrally due to2142

dominance of the effects from jets.2143

9.5 Resources2144

9.5.1 List of LO/NLO Monte Carlos/available tools2145

9.5.2 Wish list for theorists2146

Higher-order treatment of GF signal/gg–>gamma gamma interference.2147

23S. Gascon-Shotkin, M. Kado (eds.) and ; ...

November 18, 2011 – 11 : 26 DRAFT 105

mH (GeV) 110-170 170-220ATLAS ∆φll < 1.3 ∆φll < 1.8

S.R. mll < 50 GeV mll < 65 GeVATLAS mll > mZ + 15 GeV (ee,µµ)

C.R. mll > 80 GeV (eµ)CMS ...

Table 35: Definition of the signal and control regions in ATLAS and CMS analyses.

10 WW∗ decay mode242148


10.2 WW background.2150

10.3 Extrapolation parametersα.2151

The WW background is estimated formH < 200 GeV using event counts in a well defined control2152

region (C.R.). The control region is defined using cuts onmll and∆φll that exploit the spin correlation2153

of the WW pair from a spin-0 particle decay like the Higgs. Forboosted WW pairs the correlation is2154

weaker , therefore the cuts on the two variables are relaxed for higher Higgs masses. In table 35 we show2155

the cuts used by the two collaborations in differentmH intervals to define the signal and the WW C.R.2156

for the different channels.2157

The amount of WW background in signal region is determined from the control region through2158

the parameterα defined as:2159

αWW = NS.R.WW/N

C.R.WW

the value ofα is evaluated for the 0-jet and 1-jet bin. ATLAS uses the prediction from MC@NLO2160

that computes thepp → WW ∗ → lνlν at NLO including off-shell contributions and spin correlation2161

obtained with some approximation for off-shell W’s. The uncertainty onα’s is obtained computing2162

PDF and scale uncertainties. The scale uncertainties are computed using MC@NLO and varying the2163

factorisation and normalisation indipendently between 1/2 and 2. The ratio between the two is anyway2164

taken between 1/2 and 2, so that we use 7 scale combinations: (0.5,0.5), (0.5,1), (1,0.5), (1,1), (1,2),2165

(2,1), (2,2). The pdf uncertainty is taken using the CTEQ6.6error set and adding in quadrature the error2166

between the CTEQ6.6, MSTW2008 and NNPDF2.1 central values.2167

Single resonant diagram and full ME calculation of the spin correlation for off-shell W’s is not2168

performed in MC@NLO, therefore a further modelisation uncertainty is considered by comparing the2169

α parameters obtained with MCFM and MC@NLO. Being MCFM a parton level MC, effects related2170

to jets modelisation are integrated out in the comparison byremoving the jet counting cuts from the2171

comparison, the ratio of theα parameters obtained with MCFM and MC@NLO is:2172

α(MC@NLO)

α(MCFM)= 0.980 ± 0.015

where the error is due to the MC statistics, a conservartive error of 3.5% is assumed. The errors are2173

summarised in Table 36.2174

10.4 Cross section and acceptance.2175

For high value ofmH , namelymH > 200 GeV, the statistics in the WW control region becomes quite2176

small and the control region gets contaminated by a significant signal fraction. In this region a direct2177

24B. Di Micco, R. Di Nardo, A. Farilla, B. Mellado, F. Petrucci and (eds.); ...

November 18, 2011 – 11 : 26 DRAFT 106

scale pdf CTEQ 6.6 error set pdf central (CTEQ6.6, MSTW2008, NNPDF2.1)Modelisationα0jWW 2.5% 2.6% 2.7 % 3.5%α1jWW 4% 2.5% 1.4 % 3.5 %

correlation 1

Table 36: Scale and pdf uncertainties on WW extrapolation parametersα in the ATLAS analysis.

.

σ≥0 (fb) ∆σ≥0 (%) σ≥1 (fb) ∆σ≥1 (%) σ≥2 (fb) ∆σ≥2 (%) σ≥3 ∆σ≥3

532 3.3 159 6.5 41 8.7 9 11

Table 37: Inclusive muti-jet cross section computed with MC@NLO and their scale variation. The values shownare obtained for a single lepton combination. CTEQ6.6 pdfs are used in the computation.

MC@NLO ALPGENσ≥2/σ≥1 0.256 0.360σ≥3/σ≥2 0.057 0.112

Table 38: Multi-jet cross section ratios compared between MC@NLO andALPGEN.

evaluation of the WW yield in the signal region is recommended. The WW yield in jet bins can be2178

written as in the following:2179

NWW0j = σ≥0f0A0 NWW

1j = σ≥0f1A1 (64)

The valuesf0 andf1 are defined as:2180

f0 =σ≥0 − σ≥1

σ≥0f1 =

σ≥1 − σ≥2

σ≥0

The scale uncertainties onf0 andf1 are obtained propagating the uncertainties on the inclusive jet cross2181

sections (σ≥N) that are assumed uncorrelated. The cross sections are computed for jets withpT > 252182

GeV and|η| < 4.5 for the ATLAS experiment and ..... for the CMS experiment. The inclusive cross2183

section uncertainty is evaluated using MC@NLO and applyingthe scale variation prescription as above.2184

The values of the inclusive cross section obtained and theiruncertainties are shown in table 37, they have2185

been evaluated for a single lepton combination.2186

MC@NLO simulates thepp → WW + 2 jets process through the NLOpp → WW ∗ → lνlν2187

plus parton shower. This means that no ME comptation for thepp → WW + 2 jets is implemented in2188

the generator. In order to take into account mismodelisation of the parton shower MC we compare the2189

ratioσ≥2/σ≥1 andσ≥3/σ≥2 bewteen MC@NLO and ALPGEN which computes WW production cross2190

section up to three jets. The two W’s are simulated on shell byALPGEN and also spin correlation is2191

not simulated, moreover only tree level diagrams are computed by ALPGEN, therefore the comparison2192

is performed only for jet multiplicity higher than one whereALPGEN provides an ME computation for2193

the jet yield. The comparison is shown in table 38. The discrepancy between the two generators on these2194

ratios is added in quadrature to the scale variation for the 2jet and the 3 jets inclusive cross section.2195

The inclusive multi-jet uncertainties due to scale and modelisation are summarised in table 39.2196

10.5 Theoretical errors on acceptances.2197

In addition to the scale uncertainties on the jet fractions,fi, we need to evaluate also the scale uncertain-2198

ties on the acceptancesAi as defined in equation 64. These take into account scale variation effect on2199

November 18, 2011 – 11 : 26 DRAFT 107

∆σ≥0 (%) ∆σ≥1 (%) ∆σ≥2 (%) ∆σ≥3 (%)3 6 42 100

Table 39: Uncertainties on the inclusive jets cross section due to scale and modelisation for jetpT > 25 GeV and|η| < 4.5.

all other cuts except the jet counting. In order to decouple the jet bin scale uncertainty from all others,2200

the acceptance needs to be evaluated in a given jet bin. This is done in MC@NLO by requiring a jet2201

exclusive bin at the beginning of the selection and then evaluating the ratio:2202

NCUTS and jet bin/Njet bin

The maximum relative excursion of this ratio is used as the fractional acceptance scale uncertainty. In2203

ATLAS the following cuts are applied in both 0 jet and 1 jet bins formH > 220 GeV and the ee and2204

µµ channels:pT1 > 25 GeV, pT2 > 15 GeV, |η| < 2.5, EmissT > 40 GeV,∆φll < 2.6, mll < 1402205

&& |mll −mZ | > 15 GeV, while in the 0 jet channel|pTl1 + pTl2| > 30 GeV and in the 1-jet channel2206

|pTl1 + pTl2 + pTjet +EmissT | < 30 GeV cuts are added. The scale uncertainty is 5% in the 0 jet binand2207

2% in the 1 jet bin.2208

In case LO MC are used to compute the acceptance in the analysis, the LO-MC@NLO discrepancy2209

on the given acceptance value has to be added to the scale variation value.2210

10.6 PDF errors.2211

PDF errors are much smaller than scale uncertainty and are less linked to the jet activity associated to2212

the WW production. Also correlation between jet bins can be neglected. Therefore in evaluating pdf2213

uncertainties we directly compute the productfiAi, that is the relative variation in the event yield in2214

the signal region, by varying pdf in CTEQ6.6 error set and thecentral values among MSTW2008 and2215

NNPDF2.1. The uncertainty obtained is 2% for both 0 jet and 1 jet bins.2216

November 18, 2011 – 11 : 26 DRAFT 108

11 ZZ production mode 252217


TheZZ decay mode of the Standard Model Higgs gets a lower branchingfraction with respect to the2219

WW decay over the full range of the higgs mass hypotheses inspected; nevertheless the final state with2220

four leptons (electrons and muons) from theZZ decay is very clean and almost background free so it is2221

considered to be the main discovery channel at the LHC. The four lepton channel is also the most precise2222

final state to reconstruct the mass peak of the Higgs boson thanks to the high resolution of the lepton2223

momentum reconstruction with theATLAS and theCMS detectors.2224

Both ATLAS andCMS collaborations performed perspective studies in the past and published2225

also results about the direct searches of the Higgs boson inZZ to four leptons final state, after collecting2226

data in 2010 and 2011 for about 1-2 fb−1of integrated luminosity. Detailed description of the reference2227

analyses concerning four leptons final state are provided inReferences [221,222].2228

Complementary final states with two leptons and two jets, twoleptons and two neutrinos, two2229

leptons and two taus have been also inspected; they are mostly relevant for mass above the ZZ doubly-2230

resonant peak where the contribution from reducible and irreducibile background processes can be signif-2231

icantly reduced. Detailed description of the reference analyses concerning those final states are provided2232

in References [223–227]. The focus of this section is on the evaluation of the impact of some theoretical2233

issues on the predictions and on the results for the analysespreviously mentioned, and on the estimation2234

of the most important source of background (the production of ZZ) and its related uncertainties.2235

11.2 Leading order and next to leading order generators2236

BothATLAS andCMS collaborations inspected the usage and the predictions of several generator pro-2237

grams to simulate Higgs events at LHC. In this section the distributions derived by using the multi-2238

purpose generator program PYTHIA version 6.4 [228] at leading order (LO) are compared with those2239

produced by the generator program POWHEG-BOX [159] at next to leading order (NLO).2240

Events with Higgs produced via gluon fusion and vector bosonfusion mechnisms, and decaying2241

in ZZ to four leptons final state are generated by both the programs; if MZ1 is the di-lepton combination2242

from Z decay that gives the invariant mass closest to the Z boson nominal mass andMZ2 is the otherZ(∗),2243

the distributions of the tranverse momentum are compared inFigure 49 after applying the following cuts:2244

MZ1 > 50 GeV,MZ2 > 12 GeV andpT > 5 GeV, |η| < 2.5 for all the leptons . For the vector boson2245

fusion topology the predictions are different at low transverse momentum over the full Higgs mass range2246

inspected; in the case of gluon gluon fusion production, differences becomes relevant for very largeMH,2247

where anyway the MC’s are using an approximation of the Higgsline shape that can be substantially2248

different from the predicted one, as discussed in Section 15.2249

11.3 Higher orders Higgs transverse momentum spectrum2250

The total inclusive cross sections for the Higgs productionhas been computed at NNLO+NNLL [6,2251

25, 63, 135, 140–142, 147, 151, 229], and the differential cross section for the transverse momentum is2252

expected to differ with respect to the one predicted at lowerperturbative order; the Higgs boson transverse2253

momentum distribution has been computed using a technique of resummation of the large logarithmic2254

contributions appearing at transverse momenta much smaller than the Higgs boson mass [157].2255

In this section the predictions of the tool implementing this calculation at NNLL, namely HQT [157],2256

are compared with those from the NLO generator program POWHEG BOX [159], currently used by2257

theATLAS and theCMS collaborations to simulate the Higgs production and decay.The transverse2258

momentum (pT) distribution of the Higgs produced via gluon fusion is reported in Fig. 49(left) as ob-2259

tained by using the POWHEGgenerator and HQT tool; the two distributions are normalized to the gluon2260

25N. De Filippis, S. Paganis (eds.) and S. Bolognesi, T. Cheng,K. Ellis, N. Kauer, C. Mariotti, P. Nason, I. Puljak,...

November 18, 2011 – 11 : 26 DRAFT 109

Gen Higgs Pt (GeV)0 100 200 300 400 500 600

Arb

itrar

y U

nits

/ (5

GeV

)

0

0.02

0.04

0.06

0.08

0.1 H(150GeV)→ Powheg gg

H(150GeV)→ Pythia gg

Gen Higgs Pt (GeV)0 100 200 300 400 500 600

Arb

itrar

y U

nits

/ (5

GeV

)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 H(150GeV)→ Powheg VBF

H(150GeV)→ Pythia VBF

Fig. 48: Higgs transverse momentum derived with PYTHIA (LO) and POWHEG (NLO) generators for the four-lepton final state askingMZ1

> 50 GeV,MZ2> 12 GeV andpT > 5 GeV, |η| < 2.5. Plots are normalized to

the same area.

fusion cross section reported in YR1 [6]. ThepT is significantly affected over the full range and for low2261

Higgs boson masses (MH < 150 GeV); HQT gives a larger differential cross section at lowpT (pT<2262

15 GeV) with respect to POWHEG (up to 40% increment) while at largepT the opposite behaviour2263

is observed. The ratio between thepT distributions for eachpT bin can be used as a weight for the2264

POWHEG spectrum that has been used for the currentH → ZZ analyses inCMS andATLAS. The2265

ratio (or weight) is reported in Fig. 49(right) and the best fit curve is overimposed to the histogram. A2266

table with the weights for several Higgs masses andpT bins is reported in Tab. 40.2267

The difference in HiggspT spectrum affects also theMZ1 MZ2 and four leptonspT andη distri-2268

butions, thus the number of accepted events in the detector.The impact of the reweighting of POWHEG2269

events on the acceptance of the four-lepton analysis has been evaluated. The acceptance is defined by2270

the fraction of the four-lepton events passing the following cutsMZ1 > 12 GeV,MZ2 > 12 GeV and2271

pT > 5 GeV, |η| < 2.5 for leptons; the ratio between the acceptance values for POWHEG events with2272

four electrons, four muons and two electrons and two muons final state fromH → ZZ decay, when2273

turning on/off the reweighting with HQT, are shown in Fig. 50 as a function ofMH. The impact of2274

the reweighting on the acceptance amount to 1-2% at most at low Higgs masses and to at most 1% at2275

MH > 250 GeV.2276

All the previous results are estimated with the CT10 PDF [95]set and the input values from [6].2277

The predictions of the JHU generator [230] at LO (to be added) and of POWHEG generator [159,2278

231] at NLO are compared with the predictions from HNNLO [232] at NNLOpreliminary plots: powheg2279

biased by mZ1>12 GeV cut. Cut will be removedin Fig. 51-52.2280

The prediction of POWHEGare also reported after HiggspT reweighting using HQT [157] in2281

the lowpT region and HNNLO in the highpT region, as discussed previously and reported in Tab. 40.2282

As expected, the HiggspT is more soft in HNNLO than HQT in the low pT region and the effect is2283

more pronounced in the high Higgs mass case (the highpT tail matches instead with the reweighted2284

POWHEG, by construction). It is interesting to notice that,while at low mass thepT of the leptons has2285

the same behavior as the HiggspT (i.e., softer for HNNLO), at high mass HNNLO predicts a stronger2286

pT for the leptons. The mass distribution of theZ with larger mass has larger tails in HNNLO, while the2287

opposite is true for the subleadingZ mass. It is worth noticing that the HiggspT rewieghting in powheg2288

do not affect theZ invariant mass distributions. Finally the rapidity of the Higgs boson is less central in2289

HNNLO and the and the same holds for the lepton pseudroapidity, but the difference goes to zero at high2290

mass.2291

November 18, 2011 – 11 : 26 DRAFT 110

Table 40: Relative weights HqT vs POWHEG for several Higgs masses andpT values

MH [ GeV ]pT [ GeV ] 115 120 130 140 150 160 170 180 190 200 220 250 300 350 400 450 500 550 6001.0 0.76 0.77 0.97 1.01 0.94 0.96 0.90 0.92 0.84 0.83 0.85 0.720.61 0.48 0.51 0.37 0.22 0.19 0.135.0 1.27 1.27 1.27 1.27 1.25 1.22 1.23 1.22 1.21 1.21 1.18 1.181.15 1.13 1.10 1.07 1.04 1.01 0.9810.0 1.21 1.22 1.21 1.22 1.21 1.20 1.19 1.19 1.18 1.18 1.18 1.16 1.13 1.12 1.09 1.07 1.04 1.02 0.9915.0 1.16 1.16 1.17 1.17 1.17 1.16 1.16 1.16 1.16 1.15 1.16 1.14 1.12 1.11 1.09 1.07 1.05 1.02 1.0020.0 1.11 1.11 1.12 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.12 1.11 1.10 1.09 1.07 1.05 1.03 1.0125.0 1.06 1.07 1.08 1.09 1.09 1.09 1.10 1.10 1.10 1.10 1.11 1.10 1.10 1.09 1.08 1.07 1.05 1.04 1.0230.0 1.02 1.03 1.03 1.05 1.05 1.06 1.07 1.07 1.08 1.08 1.09 1.09 1.08 1.08 1.08 1.07 1.05 1.04 1.0335.0 0.98 0.98 1.00 1.01 1.02 1.03 1.04 1.04 1.05 1.05 1.06 1.07 1.07 1.08 1.07 1.06 1.06 1.05 1.0440.0 0.94 0.95 0.96 0.97 0.98 1.00 1.01 1.02 1.03 1.03 1.04 1.05 1.06 1.07 1.07 1.06 1.06 1.05 1.0445.0 0.90 0.91 0.92 0.94 0.95 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.05 1.06 1.06 1.06 1.06 1.05 1.0550.0 0.87 0.88 0.89 0.91 0.92 0.94 0.96 0.97 0.98 0.99 1.00 1.01 1.03 1.05 1.06 1.05 1.06 1.06 1.0555.0 0.84 0.85 0.86 0.88 0.89 0.92 0.93 0.94 0.95 0.96 0.98 1.00 1.02 1.04 1.05 1.05 1.06 1.06 1.0660.0 0.81 0.82 0.83 0.85 0.87 0.89 0.91 0.92 0.93 0.94 0.96 0.98 1.01 1.03 1.04 1.05 1.06 1.06 1.0665.0 0.78 0.79 0.81 0.82 0.84 0.87 0.88 0.89 0.91 0.92 0.94 0.96 1.00 1.01 1.03 1.04 1.05 1.06 1.0770.0 0.76 0.76 0.78 0.80 0.82 0.84 0.86 0.87 0.89 0.90 0.92 0.95 0.98 1.00 1.03 1.04 1.05 1.06 1.0775.0 0.73 0.74 0.76 0.78 0.80 0.82 0.84 0.85 0.87 0.88 0.90 0.93 0.97 0.99 1.02 1.03 1.05 1.06 1.0780.0 0.71 0.72 0.74 0.75 0.77 0.80 0.82 0.83 0.85 0.86 0.88 0.91 0.96 0.98 1.01 1.03 1.05 1.06 1.0785.0 0.69 0.70 0.72 0.73 0.75 0.78 0.80 0.81 0.83 0.84 0.86 0.90 0.94 0.97 1.00 1.02 1.04 1.06 1.0790.0 0.67 0.68 0.70 0.72 0.74 0.76 0.78 0.79 0.81 0.82 0.84 0.88 0.93 0.96 0.99 1.01 1.04 1.05 1.0795.0 0.66 0.67 0.68 0.70 0.72 0.74 0.76 0.77 0.79 0.80 0.82 0.86 0.92 0.95 0.98 1.01 1.03 1.05 1.07100.0 0.64 0.65 0.67 0.68 0.70 0.73 0.74 0.76 0.77 0.79 0.81 0.85 0.90 0.94 0.98 1.00 1.03 1.05 1.07105.0 0.63 0.64 0.66 0.67 0.69 0.71 0.72 0.74 0.76 0.77 0.79 0.83 0.89 0.93 0.97 0.99 1.02 1.04 1.07110.0 0.62 0.63 0.64 0.66 0.67 0.69 0.71 0.72 0.74 0.75 0.77 0.82 0.88 0.91 0.96 0.98 1.01 1.04 1.06115.0 0.61 0.62 0.63 0.64 0.66 0.68 0.69 0.71 0.72 0.74 0.76 0.80 0.86 0.90 0.94 0.98 1.01 1.03 1.06120.0 0.60 0.61 0.62 0.63 0.65 0.67 0.68 0.69 0.71 0.72 0.74 0.79 0.85 0.89 0.93 0.97 1.00 1.03 1.05125.0 0.59 0.60 0.61 0.62 0.64 0.65 0.67 0.68 0.70 0.71 0.73 0.78 0.84 0.88 0.92 0.96 0.99 1.02 1.05130.0 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.67 0.68 0.70 0.72 0.76 0.82 0.86 0.91 0.95 0.98 1.01 1.04135.0 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.66 0.67 0.68 0.70 0.75 0.81 0.85 0.90 0.94 0.97 1.00 1.03140.0 0.58 0.59 0.59 0.60 0.61 0.62 0.63 0.64 0.66 0.67 0.69 0.73 0.79 0.84 0.89 0.93 0.96 0.99 1.02145.0 0.57 0.58 0.59 0.60 0.61 0.61 0.62 0.63 0.65 0.66 0.68 0.72 0.78 0.83 0.87 0.92 0.95 0.98 1.02150.0 0.57 0.58 0.58 0.59 0.60 0.61 0.61 0.63 0.64 0.65 0.67 0.71 0.77 0.81 0.86 0.91 0.94 0.97 1.01155.0 0.57 0.58 0.58 0.59 0.59 0.60 0.61 0.62 0.63 0.64 0.66 0.69 0.75 0.80 0.85 0.89 0.93 0.96 1.00160.0 0.57 0.57 0.58 0.58 0.59 0.59 0.60 0.61 0.62 0.63 0.65 0.68 0.74 0.79 0.83 0.88 0.92 0.95 0.98165.0 0.57 0.57 0.58 0.58 0.59 0.59 0.59 0.60 0.61 0.62 0.64 0.67 0.72 0.77 0.82 0.87 0.91 0.94 0.97170.0 0.57 0.57 0.58 0.58 0.58 0.58 0.59 0.60 0.60 0.61 0.63 0.66 0.71 0.76 0.80 0.86 0.89 0.92 0.96175.0 0.57 0.57 0.57 0.58 0.58 0.58 0.58 0.59 0.60 0.61 0.62 0.64 0.69 0.74 0.79 0.84 0.88 0.91 0.95180.0 0.57 0.57 0.57 0.58 0.58 0.58 0.58 0.59 0.59 0.60 0.61 0.63 0.68 0.73 0.77 0.83 0.87 0.90 0.93185.0 0.57 0.57 0.57 0.57 0.58 0.57 0.58 0.58 0.58 0.59 0.61 0.62 0.67 0.72 0.76 0.82 0.85 0.88 0.92190.0 0.57 0.57 0.57 0.57 0.58 0.57 0.58 0.58 0.58 0.59 0.60 0.61 0.65 0.70 0.74 0.80 0.84 0.86 0.90195.0 0.57 0.57 0.57 0.57 0.58 0.57 0.58 0.58 0.58 0.58 0.60 0.60 0.64 0.69 0.73 0.79 0.82 0.85 0.88200.0 0.57 0.57 0.57 0.57 0.58 0.57 0.58 0.58 0.57 0.58 0.59 0.59 0.62 0.67 0.71 0.77 0.81 0.83 0.87205.0 0.57 0.57 0.57 0.57 0.58 0.57 0.58 0.58 0.57 0.58 0.59 0.60 0.63 0.66 0.70 0.75 0.79 0.86 0.89210.0 0.57 0.57 0.57 0.58 0.58 0.58 0.58 0.58 0.57 0.58 0.59 0.60 0.63 0.65 0.69 0.74 0.79 0.85 0.88215.0 0.57 0.57 0.57 0.58 0.58 0.58 0.58 0.58 0.57 0.58 0.59 0.60 0.63 0.65 0.69 0.74 0.78 0.84 0.87220.0 0.57 0.57 0.58 0.58 0.58 0.58 0.59 0.59 0.57 0.58 0.58 0.60 0.63 0.65 0.68 0.73 0.77 0.83 0.86225.0 0.57 0.57 0.58 0.58 0.58 0.59 0.59 0.59 0.58 0.58 0.58 0.60 0.62 0.64 0.68 0.73 0.77 0.82 0.85230.0 0.57 0.57 0.57 0.58 0.59 0.59 0.60 0.59 0.58 0.58 0.58 0.60 0.62 0.64 0.67 0.72 0.76 0.81 0.84235.0 0.57 0.57 0.57 0.58 0.59 0.60 0.60 0.60 0.58 0.58 0.59 0.60 0.62 0.64 0.67 0.72 0.76 0.80 0.84240.0 0.57 0.56 0.57 0.58 0.59 0.60 0.61 0.61 0.59 0.59 0.59 0.60 0.62 0.64 0.66 0.71 0.75 0.80 0.83245.0 0.56 0.56 0.57 0.58 0.59 0.61 0.62 0.61 0.59 0.59 0.59 0.59 0.61 0.63 0.66 0.71 0.74 0.79 0.82250.0 0.56 0.56 0.57 0.58 0.60 0.62 0.63 0.62 0.60 0.60 0.59 0.59 0.61 0.63 0.66 0.70 0.74 0.78 0.81255.0 0.56 0.55 0.57 0.58 0.59 0.62 0.62 0.62 0.60 0.60 0.59 0.59 0.61 0.63 0.65 0.70 0.73 0.77 0.80260.0 0.56 0.55 0.57 0.58 0.59 0.61 0.62 0.62 0.60 0.59 0.59 0.59 0.61 0.63 0.65 0.70 0.73 0.76 0.79265.0 0.55 0.55 0.56 0.57 0.59 0.61 0.62 0.62 0.59 0.59 0.59 0.59 0.61 0.62 0.65 0.69 0.72 0.76 0.79270.0 0.55 0.55 0.56 0.57 0.59 0.61 0.62 0.61 0.59 0.59 0.59 0.59 0.60 0.62 0.64 0.69 0.72 0.75 0.78275.0 0.55 0.55 0.56 0.57 0.59 0.61 0.62 0.61 0.59 0.59 0.58 0.59 0.60 0.62 0.64 0.68 0.71 0.74 0.77280.0 0.55 0.54 0.56 0.57 0.58 0.61 0.61 0.61 0.59 0.59 0.58 0.59 0.60 0.62 0.64 0.68 0.71 0.74 0.77285.0 0.55 0.54 0.56 0.57 0.58 0.60 0.61 0.61 0.59 0.58 0.58 0.59 0.60 0.61 0.63 0.68 0.70 0.73 0.76290.0 0.54 0.54 0.55 0.56 0.58 0.60 0.61 0.61 0.58 0.58 0.58 0.59 0.60 0.61 0.63 0.67 0.70 0.72 0.75295.0 0.54 0.54 0.55 0.56 0.58 0.60 0.61 0.60 0.58 0.58 0.58 0.58 0.60 0.61 0.63 0.67 0.69 0.72 0.75300.0 0.54 0.54 0.55 0.56 0.58 0.60 0.61 0.60 0.58 0.58 0.57 0.58 0.60 0.61 0.63 0.67 0.69 0.71 0.74305.0 0.54 0.53 0.55 0.56 0.57 0.60 0.60 0.60 0.58 0.58 0.57 0.58 0.60 0.61 0.62 0.66 0.68 0.71 0.74310.0 0.54 0.53 0.55 0.56 0.57 0.59 0.60 0.60 0.58 0.57 0.57 0.58 0.60 0.60 0.62 0.66 0.68 0.70 0.73315.0 0.53 0.53 0.54 0.55 0.57 0.59 0.60 0.60 0.57 0.57 0.57 0.58 0.59 0.60 0.62 0.66 0.67 0.70 0.73320.0 0.53 0.53 0.54 0.55 0.57 0.59 0.60 0.59 0.57 0.57 0.57 0.58 0.59 0.60 0.62 0.65 0.67 0.69 0.72325.0 0.53 0.53 0.54 0.55 0.57 0.59 0.60 0.59 0.57 0.57 0.56 0.58 0.59 0.60 0.62 0.65 0.67 0.69 0.72330.0 0.53 0.52 0.54 0.55 0.56 0.59 0.59 0.59 0.57 0.57 0.56 0.58 0.59 0.60 0.62 0.65 0.66 0.69 0.71335.0 0.53 0.52 0.54 0.55 0.56 0.58 0.59 0.59 0.57 0.56 0.56 0.58 0.59 0.60 0.61 0.65 0.66 0.68 0.71340.0 0.52 0.52 0.53 0.54 0.56 0.58 0.59 0.59 0.56 0.56 0.56 0.58 0.59 0.60 0.61 0.64 0.66 0.68 0.70345.0 0.52 0.52 0.53 0.54 0.56 0.58 0.59 0.58 0.56 0.56 0.56 0.58 0.59 0.59 0.61 0.64 0.65 0.67 0.70350.0 0.52 0.52 0.53 0.54 0.56 0.58 0.59 0.58 0.56 0.56 0.55 0.58 0.59 0.59 0.61 0.64 0.65 0.67 0.70355.0 0.52 0.51 0.53 0.54 0.55 0.58 0.58 0.58 0.56 0.56 0.55 0.58 0.59 0.59 0.61 0.64 0.65 0.67 0.69360.0 0.52 0.51 0.53 0.54 0.55 0.57 0.58 0.58 0.56 0.55 0.55 0.58 0.59 0.59 0.61 0.64 0.64 0.67 0.69365.0 0.51 0.51 0.52 0.53 0.55 0.57 0.58 0.58 0.55 0.55 0.55 0.58 0.59 0.59 0.61 0.63 0.64 0.66 0.69370.0 0.51 0.51 0.52 0.53 0.55 0.57 0.58 0.57 0.55 0.55 0.55 0.58 0.59 0.59 0.61 0.63 0.64 0.66 0.68375.0 0.51 0.51 0.52 0.53 0.55 0.57 0.58 0.57 0.55 0.55 0.54 0.58 0.59 0.59 0.61 0.63 0.64 0.66 0.68380.0 0.51 0.50 0.52 0.53 0.54 0.57 0.57 0.57 0.55 0.55 0.54 0.58 0.59 0.59 0.61 0.63 0.63 0.66 0.68385.0 0.51 0.50 0.52 0.53 0.54 0.56 0.57 0.57 0.55 0.54 0.54 0.58 0.60 0.59 0.61 0.63 0.63 0.65 0.68390.0 0.50 0.50 0.51 0.52 0.54 0.56 0.57 0.57 0.54 0.54 0.54 0.58 0.60 0.59 0.61 0.63 0.63 0.65 0.68395.0 0.50 0.50 0.51 0.52 0.54 0.56 0.57 0.56 0.54 0.54 0.54 0.58 0.60 0.59 0.61 0.63 0.63 0.65 0.68400.0 0.50 0.50 0.51 0.52 0.54 0.56 0.57 0.56 0.54 0.54 0.53 0.58 0.60 0.59 0.61 0.62 0.63 0.65 0.68

November 18, 2011 – 11 : 26 DRAFT 111

(GeV/c)T

p0 100 200 300 400 500

(p

b/ 1

GeV

/c)

TdN

/dp

0

0.05

0.1

0.15

0.2

0.25

0.3HqT 2.0

POWHEG + PYTHIA2 = 150 GeV/cHm

(YR)HσNormalized to

(GeV/c)T

p1 10 210

HqT

/PO

WH

EG

wei

ght

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Fig. 49: (Left) pT spectrum of the SM Higgs boson of massMH = 150 GeV produced via gluon-gluon fusion asobtained by using the POWHEG generator and HQT tool. (Right) the ratio HQT vs POWHEG as a function ofthe Higgs bosonpT.

11.4 TheZZ background process2292

The understanding of the background processes from the theoretical and the experimental sides is manda-2293

tory to be able to perform a search of new physics.2294

The main goal of this section is to compare the predictions from different generators for theZZ2295

process (in particular for the four lepton final state). The production of two Z bosons represents the2296

irreducible background for the direct searches of the Higgsboson in theH → ZZ channels at LHC.2297

For this study we coherently used the Standard Model input parameters as speficied in the Ap-2298

pendix of Ref. [6]. The PDF’s used are: CT10, NNPdf2.0 and MSTW2008. The central value of the2299

cross section and the uncertainty originating from the PDF are estimated following the PDF4LHC pre-2300

scription [90] In order to estimate the QCD scale uncertainty the MSTW2008 PDF has been used as2301

central value and the QCD scale is varied following the prescription of [6].2302

The distributions for comparison and the theoretical uncertainties are calculated for a few sets of2303

cuts:2304

– Cut1:MZ1 > 12 GeV andMZ2 > 12 GeV2305

– Cut2:MZ1 > 50 GeV,MZ2 > 12 GeV,pT(l) > 5 GeV, |η(l)| < 2.52306

– Cut3:60 < MZ1 < 120 GeV and60 < MZ2 < 120 GeV.2307

11.4.1 qq → ZZ generators2308

11.4.1.1 MCFM predictions2309

The MCFM program [163, 233, 234] v6.1 computes the cross section at LO and NLO for the process2310

qq → ZZ including ZZ, Zγ∗ and their interference, for the double resonant (or t-channel) and single2311

resonant (or s-channel) diagrams, and for the processgg → ZZ.2312

Fig. 53 (left) shows the four leptons invariant mass distribution obtained with MCFM at LO for2313

ZZ production, including or not the single resonant (or s-channel) contribution. The prediction without2314

the single resonant contribution is obtained by running MCFM v5.8. The “Cut1” selection is applied,2315

i.e.mll > 12 GeV.2316

At LO the cross section as a function ofm2e2µ for the processqq → ZZ → 2e2µ is shown in2317

Fig. 53 (right) and for three different set of cuts. The blackline corresponds to the “Cut1” selection, i.e.2318

mll > 12 GeV, that is the minimal cut requested in the analyses to subtract the contribution to heavy2319

November 18, 2011 – 11 : 26 DRAFT 112

]2 [GeV/cHM

100 200 300 400 500 600

Acc

epta

nce

wei

ghte

d / u

nwei

ghte

d

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

µ 2e2→ ZZ →H

µ 4→ ZZ →H

4e→ ZZ →H

µ|<2.5 for e/η>5 GeV/c, |T

p

Fig. 50: Ratio between the acceptance values for POWHEG events with four electrons, four muons and twoelectrons and two muons final state fromH → ZZ decay, when turning on/off the reweighting with HQT.

flavour resonances decaying into leptons. The blue line is obtained taking into account the acceptance2320

of the detectors, thus asking the leptons to havepT > 5 GeV andη < 2.5 (“Cut2” selection). The2321

red line is the differential cross section for the production of two Z boson, both on shell, i.e. asking2322

60 GeV< mll < 120 GeV (“Cut3” selection).2323

Figure 54 (left) shows the cross section at NLO for the full processpp → ZZ(∗) → 2e2µ, and2324

for thegg contribution separately in the insert, as a function of the invariant mass of the 4 leptons. The2325

peak at 91 GeV is dominated by the contribution of the single resonant (or s-channel) diagram, while for2326

m4l > 100 GeV the double resonant diagrams (or t-channel) are essentially the only contribution.2327

In Figure 54 (right) the cross section form2e2µ from MCFM v6.1 is show for three different2328

set of cuts for the double resonant region only: the black line is askingmll > 12 GeV, that is the2329

minimal cut requested in the analyses to subtract the contribution to heavy flavour resonances decaying2330

into leptons. The red line is taking into account the acceptance of the detectors, thus asking the leptons2331

to havepT > 5 GeV andη < 2.5. The blue line is the differential cross section for the production of2332

November 18, 2011 – 11 : 26 DRAFT 113

[GeV]T

Higgs p0 50 100 150 200 250 300 350 400 450 500

arbi

trar

y no

rmal

izat

ion

-510

-410

-310

-210

-110

[GeV]T

Higgs p0 50 100 150 200 250 300 350 400 450 500

arbi

trar

y no

rmal

izat

ion

-310

-210

-110

[GeV]T

leading lepton p0 20 40 60 80 100 120 140 160 180 200

arbi

trar

y no

rmal

izat

ion

-410

-310

-210

-110

[GeV]T

leading lepton p0 20 40 60 80 100 120 140 160 180 200

arbi

trar

y no

rmal

izat

ion

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

larger Z mass0 20 40 60 80 100 120

arbi

trar

y no

rmal

izat

ion

-610

-510

-410

-310

-210

-110

larger Z mass0 20 40 60 80 100 120

arbi

trar

y no

rmal

izat

ion

-610

-510

-410

-310

-210

-110

smaller Z mass0 10 20 30 40 50 60

arbi

trar

y no

rmal

izat

ion

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

smaller Z mass0 20 40 60 80 100 120

arbi

trar

y no

rmal

izat

ion

-510

-410

-310

-210

-110

Fig. 51: Differential distributions (in arbitrary units) at7 TeV for Higgs mass 200 GeV (left) and 500 GeV (right)for three different Monte Carlo generators: POWHEG (black), HNNLO (red), POWHEG reweighted with Hqt andHNNLO (shaded blue).

November 18, 2011 – 11 : 26 DRAFT 114

Higgs rapidity0 0.5 1 1.5 2 2.5 3 3.5

arbi

trar

y no

rmal

izat

ion

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Higgs rapidity0 0.5 1 1.5 2 2.5 3 3.5

arbi

trar

y no

rmal

izat

ion

0

0.05

0.1

0.15

0.2

leading lepton pseudorapidity-5 -4 -3 -2 -1 0 1 2 3 4 5

arbi

trar

y no

rmal

izat

ion

0

0.01

0.02

0.03

0.04

0.05

0.06

leading lepton pseudorapidity-5 -4 -3 -2 -1 0 1 2 3 4 5

arbi

trar

y no

rmal

izat

ion

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Fig. 52: Differential distributions (in arbitrary units) at7 TeV for Higgs mass 200 GeV (left) and 500 GeV (right)for three different Monte Carlo generators: POWHEG (black), HNNLO (red), POWHEG reweighted with Hqt andHNNLO (shaded blue).

[GeV] 4lM

100 200 300 400 500

)

-2 1

0!

/dM

(fb

) (

!d

1

10

210v6.0

v5.8

MCFM (LO)""ee"Z*Z*"pp

>12 GeV2lM

With single-resonant diagram

Fig. 53: (left) The cross sections forqq → ZZ(∗) → 2e2µ as a function ofm2e2µ at 7 TeV from MCFM for thefull calculation and without the single resonant contribution; (Right) LO cross sections forqq → ZZ(∗) → 2e2µ

as a function ofm2e2µ at7 TeV from MCFM at LO.

November 18, 2011 – 11 : 26 DRAFT 115

Fig. 54: (Left) The cross sections forZZ(∗) production as a function ofm2e2µ at 7 TeV from MCFM at NLO;(right) cross sections forZZ(∗) production as a function ofm2e2µ at7 TeV from MCFM at NLO for three differentsets of cuts as described in the text.

two Z boson, both on shell, i.e. asking60 GeV< mll < 120 GeV.2333

11.4.1.2 POWHEGpredictions2334

In POWHEG BOX [159] a new implementation of the vector boson pair production process at NLO has2335

been provided [231].Z/γ∗ interference as well as single resonant contribution are properly included.2336

Interference terms arising from identical leptons in the final state are considered.2337

In figure 55 the 4 leptons invariant mass distributions for the final state2e2µ are shown for2338

POWHEG, using two different PDF (MSTW and CT10), and compared with MCFM v6.1. The plot on2339

the left is obtained askingmll > 12 GeV, i.e. the Cut1. The plot on the right is asking the second sets2340

of cuts, Cut2. The two programs show a very good agreement. The difference due to the different PDF2341

is discussed in section 11.4.4.2342

In Figure 56 them4l distribution is shown for the2e2µ and4e final states in order to see the effect2343

of the interference between identical leptons. The top two figures are obtained with the Cut1 selection,2344

while the lower ones with Cut2 selection. The effects of using two different PDF is also seen.2345

A full comparison has been also performed between the predictions of both POWHEG at NLO2346

and PYTHIA at LO; that is shown in Fig. 57 (left) and the disitributions are normalized to the the2347

corresponding cross sections. The difference come from thelack of the single resonant contribution in2348

PYTHIA and the LO calculations for the doubly resonant contribution.2349

The impact of the interference in theZZ → 4µ channel with identical leptons is shown in Fig. 572350

(right).The total cross section increases of about 4% because of the interference.2351

11.4.2 gg → ZZ generators2352

The gluon-induced ZZ background, although technically of NNLO compared to the first order Z-pair2353

production, amounts to a substantial fraction to the total irreducible background. Taking into account2354

these diagrams, a full NNLO calculation for the processqq → ZZ is not available. Therefore the con-2355

tributions of these diagrams are estimated by using MCFMV6.1 and the dedicated tool GG2ZZ [235],2356

which computes thegg → ZZ at LO, which is of orderα2s , compared toα0

s for the LOqq → ZZ.2357

The GG2ZZ tool provides the functionality to compute the cross-section after applying a cut on2358

November 18, 2011 – 11 : 26 DRAFT 116

2 , GeV/c4lm100 200 300 400 500 600

)-1

Eve

nts/

10G

eV (

Nor

mal

ized

to 1

fb

-110

1

10 >12GeVLLm

MSTW POWHEG 2e2mu

MSTW MCFM 2e2mu

CT10 POWHEG 2e2mu

CT10 MCFM 2e2mu

2 , GeV/c4lm100 200 300 400 500 600

)-1

Eve

nts/

10G

eV (

Nor

mal

ized

to 1

fb

-210

-110

1

|<2.5L

>5GeV, |etaL

>12GeV, pT2

>50GeV, mZ1mZ

MSTW POWHEG 2e2mu

MSTW MCFM 2e2mu

CT10 POWHEG 2e2mu

CT10 MCFM 2e2mu

Fig. 55: ZZ → 2e2µ invariant mass distributions at7 TeV with POWHEG and MCFMV6.1. Two differentPDF are used. The left plots are obtained asking onlym2l > 12 GeV and the right plots askingMZ1

> 50 GeV,MZ2

> 12 GeV,pT(l) > 5 GeV, |η(l)| < 2.5

the mimimally generated invariant mass of the same-flavour lepton pairs (which can be interpreted as the2359

Z/γ invariant mass)mminℓℓ = 12 GeV.2360

11.4.3 gg → ZZ: Comparison ofGG2ZZ and MCFM2361

In this section, a comparison of results for thegg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′ (ℓ: charged lepton) continuum2362

background calculated at LO withGG2ZZ and MCFM is presented.26 The MCFM calculation of thegg2363

subprocess is described in Ref. [234]. MCFM also includes a NLO calculation of theqq subprocess [233,2364

234]. ForGG2ZZ, first results have been presented in Ref. [235].GG2ZZ employs the same calculational2365

techniques asGG2WW [237,238]. Due to the Landau-Yang theorem, all graphs with ggV triangle quark2366

loop (including those withs-channelZ propagator) vanish. The MCFM calculation exploits that thetop2367

quark decouples in good approximation. Thet contribution to the quark loop is therefore neglected. The2368

b contribution is included in the massless limit. InGG2ZZ, theb andt contributions are included with2369

finite masses.2370

Parton-level cross sections andMZ,Z distributions forpp collisions at√s = 7 TeV are compared2371

for three set of cuts. In addition, apT(Z) > 0.05 GeV cut is applied to prevent that numerical insta-2372

bilities spoil the amplitude evaluation. This technical cut reduces the cross sections by at most 0.05%.2373

Results are given for a single lepton flavour combination, e.g. ℓ = e−, ℓ′ = µ−. Lepton masses are ne-2374

glected. The input parameter set of Ref. [6], App. A, is used.The renormalisation and factorisation scales2375

are set toMZ. The PDF set MSTW2008 NNLO with 3-loop running forαs(µ2) andαs(M

2Z) = 0.117072376

is used. The fixed-width prescription is used forZ propagators.2377

For cut sets “Cut1”, “Cut2” and “Cut3”, results calculated with gg2ZZ and MCFM are shown2378

in Tab. 41 (left) (cross section) and Fig. 58 (MZ,Z distribution). The cross sections agree up to 1% or2379

better. Nevertheless, the residual deviations are significant relative to the MC integration errors. The2380

MZ,Z distributions agree, except in the vicinity of the peaks at 50 and 200 GeV. In these invariant mass2381

regions, MCFM’s differential cross section is slightly larger than gg2ZZ’s. Tab. 42 and Fig. 58 (right)2382

demonstrate that the observed deviations are consistent with differences of the calculations in gg2ZZ and2383

26Off-shell results for the same-flavour processgg → ZZ → ℓℓℓℓ have been presented in Ref. [236].

November 18, 2011 – 11 : 26 DRAFT 117

2 , GeV/c4lm100 200 300 400 500 600

)-1

Eve

nts/

10G

eV (

Nor

mal

ized

to 1

fb

-110

1

10 >12GeVLLm

MSTW POWHEG 2e2mu

MSTW POWHEG 2e2mu

CT10 POWHEG 2e2mu

MSTW POWHEG 4e

CT10 POWHEG 4e

2 , GeV/c4lm100 200 300 400 500 600

2e2m

uσ/

4eσR

atio

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 MSTW POWHEG 4e/POWHEG 2e2mu

CT10 POWHEG 4e/POWHEG 2e2mu

2 , GeV/c4lm100 200 300 400 500 600

)-1

Eve

nts/

10G

eV (

Nor

mal

ized

to 1

fb

-210

-110

1

|<2.5L

>5GeV, |etaL

>12GeV, pT2

>50GeV, mZ1mZ

MSTW POWHEG

CT10 POWHEG

MSTW POWHEG

CT10 POWHEG

2 , GeV/c4lm100 200 300 400 500 600

2e2m

uσ/

4eσR

atio

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 MSTW POWHEG 4e/POWHEG 2e2mu

CT10 POWHEG 4e/POWHEG 2e2mu

Fig. 56: ZZ → 2e2µ andZZ → 4e invariant mass distributions and their ratio at7 TeV with POWHEG. Twodifferent PDF are used. The upper plots are obtained asking only m2l > 12 GeV and the lower plots askingMZ1

> 50 GeV,MZ2> 12 GeV,pT(l) > 5 GeV, |η(l)| < 2.5

November 18, 2011 – 11 : 26 DRAFT 118

]2 [GeV/cZZm

0 100 200 300 400 500 600

]2 [b

in =

6 G

eV/c

ZZ

dN/d

m

-410

-310

-210 POWHEG (NLO)

PYTHIA (LO)

]2 [GeV/cZZm

0 100 200 300 400 500 600

]2 [b

in =

6 G

eV/c

ZZ

dN/d

m

-510

-410

-310 with interfµPOWHEG: 4

with no interfµPOWHEG: 4

Fig. 57: ZZ → 4µ invariant mass distributions at7 TeV as derived by PYTHIA and POWHEG (left) and turningon/off in POWHEG the interference contribution for identical leptons (right)

Table 41: Cross sections in fb forgg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′ in pp collisions at√s = 7 TeV and a single lepton

flavour combination calculated at LO with gg2ZZ-2.0 and MCFM-6.1. Three cut sets are applied:MZ1 > 12

GeV,MZ2 > 12 GeV (Cut1);MZ1 > 50 GeV,MZ2 > 12 GeV, pT(ℓ) > 5 GeV, |η(ℓ)| < 2.5 (Cut2);60 GeV< MZ1 < 120 GeV,60 GeV< MZ2 < 120 GeV (Cut3).

σ(gg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′) [fb], pp,√s = 7 TeV

gg2ZZ-2.0 MCFM-6.1 σMCFM/σgg2ZZ

cuts 1 1.157(2) 1.168(2) 1.010(2)

cuts 2 0.6317(4) 0.6293(4) 0.9962(8)

cuts 3 0.8328(3) 0.8343(3) 1.0019(5)

MCFM as discussed above. In the limitmb → 0 andmt → ∞, gg2ZZ’s results are expected to agree2384

with MCFM’s results within MC integration errors. In Tab. 42and Fig. 58 (right), this is confirmed for2385

cut set 1. Note that for cut sets 1 and 3 the finite mass effects decrease the cross section, while for cut set2386

2 the cross section is increased (see Tab. 41).272387

11.4.4 Theoretical uncertainties2388

PDF+αs and QCD scale uncertainties forpp → ZZ → 2e2µ at NLO andgg → ZZ → 2e2µ are2389

evaluated using MCFM version 6.1. The following cuts are applied to the leptons:mee > 12,mµµ > 12,2390

electrons’pT > 7 and|η| < 2.5, and muons’pT > 5 and|η| < 2.4.2391

For the estimation of the PDF+αs systematic errors, the PDF4LHC prescription [90] is ap-2392

plied. The upper and lower edges of the envelop are computed by the three PDF sets: CT10 [92],2393

MSTW08 [95], NNPDF [84], which can be parametrized as follows:2394

27For cut set 2, one obtains 0.6297(4) fb with gg2ZZ-2.0 andmt = 105 GeV,mb = 10−4 GeV, which agrees with MCFM-6.1’s result.

November 18, 2011 – 11 : 26 DRAFT 119

Table 42: Finite b andt mass effects for the cross section ofgg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′ when cut set Cut1 isapplied. Other details in Tab. 41.

cuts 1:MZ1 > 12 GeV,MZ2 > 12 GeV σ [fb] σMCFM/σgg2ZZ

gg2ZZ-2.0 (mt = 172.5 GeV,mb = 4.75 GeV) 1.157(2) 1.010(2)

MCFM-6.1 (5 massless quark flavours) 1.168(2) —

gg2ZZ-2.0 (mt = 105 GeV,mb = 10−4 GeV) 1.1677(8) 1.001(2)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 50 100 150 200 250 300 350 400 450 500

MZZ [GeV]

∗ = pT (ℓ) > 5 GeV, |η(ℓ)| < 2.5

gg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′

LO, pp,√s = 7 TeV

gg2ZZ-2.0 (dashed)

MCFM-6.1 (solid)

dσdMZZ[fb

GeV

]MZ1 > 12 GeV, MZ2 > 12 GeVMZ1 > 50 GeV, MZ2 > 12 GeV, ∗60 GeV < MZ1, MZ2 < 120 GeV

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 50 100 150 200 250 300 350 400 450 500

MZZ [GeV]

MZ1 > 12 GeV, MZ2 > 12 GeV

gg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′

LO, pp,√s = 7 TeV

dσdMZZ[fb

GeV

]gg2ZZ-2.0 (Mt = 172.5 GeV, Mb = 4.75 GeV)

MCFM-6.1 (5 massless quark flavours)

gg2ZZ-2.0 (Mt = 105 GeV, Mb = 10−4 GeV)

Fig. 58: (left)MZ,Z distributions forgg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′ calculated with MCFM-6.1 (Cut1: black, Cut2:blue, Cut3: red) andGG2ZZ-2.0 (Cut1: green dashed, Cut2: cyan dashed, Cut3: magenta dashed). Other detailsas in Tab. 41; (right) Finiteb andtmass effects for theMZ,Z distribution ofgg → Z(γ∗)Z(γ∗) → ℓℓℓ′ℓ′ when cutset Cut1 is applied. Other details as in Tab. 41.

ZZ@NLO :κ(m4ℓ) = 1 + 0.0035√

(m4ℓ − 30) (65)2395

gg → ZZ :κ(m4ℓ) = 1 + 0.0066√

(m4ℓ − 10) (66)

In figure 59 the difference between the central value of the cross section and the cross section2396

computed with the 3 different PDF varying them by plus and minus 1σ for qq → ZZ(∗) → m2e2µ (left)2397

and forgg → ZZ(∗) → m2e2µ (right) as a function ofm2e2µ at7 TeV.2398

In figure 60 the uncertainty arising from the PDF+αs choice following the PDF4LHC prescription2399

is shown as a function of the invariant mass of the 4 leptons for theqq andgg initial states.The red line2400

is the parametrization from Eq. 65 and Eq. 66.2401

For the estimation of QCD scale systematic errors, we calculate variations in the differential cross2402

sectiondσ/dm4ℓ as the renormalization and factorization scales is changedby a factor of two up and2403

down from their default valueµR = µF = MZ. The four-lepton mass dependent QCD scale systematic2404

errors can be parametrized as follows:2405

ZZ@NLO :κ(m4ℓ) = 1.00 + 0.01√

(m4ℓ − 20)/13 (67)2406

gg → ZZ :κ(m4ℓ) = 1.04 + 0.10√

(m4ℓ + 40)/40) (68)

In Figure 61 the cross section forqq → ZZ(∗) → m2e2µ (left) and forgg → ZZ(∗) → m2e2µ2407

(right) is shown as a function ofm2e2µ at7 TeV from MCFM computed with the CT10 PDF and varying2408

November 18, 2011 – 11 : 26 DRAFT 120

2, GeV/c4lm100 150 200 250 300 350 400 450 500 550 600

(NLO

)en

vδ

1 +

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2CT10 central value / Mid-point

MSTW central value / Mid-point

NNPDF central value / Mid-point

2, GeV/c4lm100 150 200 250 300 350 400 450 500 550 600

(gg)

env

δ1

+ gg

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Fig. 59: The difference between the central value of the cross section and the cross section computed with 3different PDF forqq → ZZ(∗) → m2e2µ (left) and forgg → ZZ(∗) → m2e2µ (right) as a function ofm2e2µ at7 TeV from MCFM.

2 , GeV/c4lm100 150 200 250 300 350 400 450 500 550 600

(NLO

)en

vδ

1 +

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

2 , GeV/c4lm100 150 200 250 300 350 400 450 500 550 600

(gg)

env

δ1

+

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Fig. 60: The difference between the central value of the cross section and the cross section computed with plusand minus 1σ of the total PDF+αs variation, following the PDF4LHC prescription, forqq → ZZ(∗) → m2e2µ

(left) and forgg → ZZ(∗) → m2e2µ (right) as a function ofm2e2µ at 7 TeV from MCFM. The red line is theparametrization described in the text.

November 18, 2011 – 11 : 26 DRAFT 121

2 , GeV/c4l

Four-lepton mass m100 200 300 400 500 600

)-1

NLO

Eve

nts

( N

orm

aliz

ed to

1 fb

-210

-110

1

NLO CT10 Scale=45

NLO CT10 Scale=91

NLO CT10 Scale=182

2 , GeV/c4l


)-1

gg E

vent

s (

Nor

mal

ized

to 1

fb

-310

-210

-110gg CT10 Scale=45

gg CT10 Scale=91

gg CT10 Scale=182

Fig. 61: The cross section forqq → ZZ(∗) → m2e2µ (left) and forgg → ZZ(∗) → m2e2µ (right) as a function ofm2e2µ at7 TeV from MCFM computed with the CT10 PDF and varying the QCD scale by a factor of two.

the QCD scale by a factor of two. In figure 62 the ratio of the cross section computed at the different2409

scale and the cross section computed at the central value of the QCD scale (i.e. atMZ) is shown as a2410

function of the four lepton invariant mass. The red lines arethe parametrization from Eq. 67 and Eq. 68 .2411

11.4.5 Summary2412

Average uncertainties (for the full 4l-mass spectrum)2413

Variation of uncertainties across the 4l-mass spectrum2414

Produce results for direct qq/gg ZZ production as well as normalized to the qq Z product ion2415

November 18, 2011 – 11 : 26 DRAFT 122

2 , GeV/c4l


)Z

(mσ(Q

) /

σN

LO R

atio

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

ZQ = 2 m

/ 2ZQ = m

2 , GeV/c4l


)Z

(mσ(Q

) /

σgg

Rat

io

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

ZQ = 2 m

/ 2ZQ = m

Fig. 62: The ratio of the cross sections computed at different scalesand the cross section computed at central valueof the QCD scale forqq → ZZ(∗) → m2e2µ (left) andgg → ZZ(∗) → m2e2µ (right) as a function ofm2e2µ at7 TeV from MCFM. The red line is the parametrization describedin the text

November 18, 2011 – 11 : 26 DRAFT 123

12 Higgs boson production in the MSSM282416

12.1 The MSSM Higgs sector: general features2417

Within the Minimal Supersymmetric Standard Model (MSSM) the Higgs boson sector contains, contrary2418

to the SM, two scalar doublets, accommodating five physical Higgs bosons. These are, at lowest order,2419

the light and heavy CP-evenh andH, the CP-oddA, and the charged Higgs bosonsH±. At the tree-level2420

the MSSM Higgs sector can be expressed in terms of the SM gaugecouplings and two further input2421

parameters, conventionally chosen astan β ≡ v2/v1, the ratio of the two vacuum expectation values,2422

and eitherMA or MH±. Consequently, all other masses and mixing angles can be predicted. However,2423

the Higgs sector of the MSSM is affected by large higher-order corrections, which have to be taken into2424

account for reliable phenomenological predictions. The higher-order corrections arise in particular due2425

to the large top Yukawa coupling, leading to large loop contributions from the top and stop sector to the2426

Higgs masses and couplings. Similarly, for large values oftan β also effects from the bottom/sbottom2427

sector can be large. These corrections are also affected by the relation between the bottom quark mass and2428

the bottom Yukawa coupling, which receivestan β-enhanced contribution entering via∆b [239–243].2429

These correcttions are non-vanishing even in the limit of asymptotically large values of the SUSY mass2430

parameters. For the light Higgs boson these corrections vanish if also the Higgs boson mass scale,MA2431

or MH± goes to large vaules. An analoguous contribution, althoughin general smaller, exists for theτ2432

lepton. The MSSM Higgs sector is CP-conserving at lowest order. However, CP-violating effects can2433

enter via the potentially large loop corrections. In this case all three neutral Higgs bosons mix with each2434

other. As in Ref. [6] we will focus here on the CP-conserving case and useMA as input parameter.2435

In a large part of the MSSM parameter space the couplings of the light CP-even Higgs boson to2436

SM gauge bosons and fermions become SM-like. This decoupling limit is reached forMA ≫ MZ,2437

however in practice realised already forMA>∼ 2MZ. Consequently, in this parameter region the light2438

CP-even Higgs boson of the MSSM resembles the Higgs boson of the SM. Results for the light CP-2439

even Higgs boson production cross sections and decay branching ratios approach the corresponding SM2440

values, provided that the additional SUSY mass scales are too high to affect the Higgs production and2441

decay.2442

However, in general the Higgs phenomenology in the MSSM can differ very significantly from2443

the SM case. Depending onMA and the SUSY mass scales, the relevant couplings entering production2444

and decay processes of an MSSM Higgs boson can be much different from the corresponding couplings2445

in the SM case. Consequently, the lower bound on the Higgs mass in the SM from the searches at LEP2446

cannot directly be applied to the MSSM case [244, 245]; much lighter Higgs masses are possible in the2447

MSSM without being in conflict with the present search limits. Furthermore, the presence of more than2448

one Higgs boson in the spectrum can give rise to overlapping signals in the Higgs searches, in particular2449

in parameter regions where the Higgs-boson widths are large.2450

Due to the enlarged spectrum in the MSSM, further productionand decay processes are possible2451

compared to the SM case. In particular, MSSM Higgs bosons canbe produced in association with or2452

in decays of SUSY particles, and decays of MSSM Higgs bosons into SUSY particles, if kinematically2453

allowed, can have a large impact on the Higgs branching ratios. In certain parts of the parameter space2454

also decays of heavy MSSM Higgs bosons into lighter Higgs canbecome important. These decays could2455

potentially yield valuable information on the Higgs self-couplings. However, In the following we will2456

mainly focus on the production processes that are expected to be most relevant for early searches for2457

MSSM Higgs bosons at the LHC. These are the Higgs production in gluon fusion for the light CP-even2458

Higgs boson and the production in association with bottom quarks, which can be relevant for all three2459

neutral Higgs bosons. Corresponding results for the total cross sections were presented in Ref. [6].2460

Due to the large number of free parameters in the MSSM, it is customary to interpret searches for2461

28M. Spira, M. Vazquez Acosta, M. Warsinsky, G. Weiglein (eds.); E.A. Bagnashci, M. Cutajar, G. Degrassi, S. Dittmaier,R. Harlander, S. Heinemeyer, M. Krämer, A. Nikitenko, S. Palmer, P. Slavich, A. Vicini, M. Wiesemann . . .

November 18, 2011 – 11 : 26 DRAFT 124

the Higgs bosons in terms of benchmark scenarios where the lowest-order input parameterstan β and2462

MA (orMH±) are varied, while the other SUSY parameters entering via radiative corrections are set to2463

certain benchmark values. In the following we will focus on themmaxh benchmark scenario [7]. Within2464

the on-shell scheme it is defined as292465

MSUSY = 1 TeV, Xt = 2MSUSY, µ = 200 GeV, Mg = 800 GeV, M2 = 200 GeV, Ab = At, (69)

whereMSUSY denotes the common soft-SUSY-breaking squark mass of the third generation,Xt =2466

At−µ/ tan β the stop mixing parameter,At andAb the stop and sbottom trilinear couplings, respectively,2467

µ the Higgsino mass parameter,Mg the gluino mass, andM2 the SU(2)-gaugino mass parameter.2468

While in the SM the Higgs boson mass is a free input parameter,in the MSSM all masses, mixings2469

and couplings can be calculated in terms of the other model parameters. Consequently, calculations of2470

Higgs production and decay processes in the MSSM require as afirst step the evaluation of the Higgs-2471

boson masses and mixing contributions in terms ofMA, tan β and all other SUSY relevant parameters2472

that enter via radiative corrections. Furthermore, the mixing between the different (neutral) Higgs boson2473

must be taken into account in order to ensure the correct on-shell properties of the Higgs fields appearing2474

in the S-matrix elements of production or decay processes. To perfrom this kind of evaluations in terms of2475

the MSSM input parameters, two dedicated codes exist, FEYNHIGGS [74–77] and CPSUPERH [78,79].2476

Both incorporate higher-order corrections in the MSSM Higgs sector up to the two-loop level. In the2477

case of real parameters a more complete set of higher-order corrections is included in FEYNHIGGS,2478

which was chosen for the corresponding calculations in Ref.[6]. Following previous evalutions, we use2479

FEYNHIGGS to calculate the Higgs-boson masses and effective couplings in the MSSM also here. A brief2480

comparison of the two codes and the respective differences in themmaxh and no-mixing benchmark can be2481

found in Ref. [6]. The thus derived parameters can be passed via the SUSY Les Houches Accord [80,81]2482

to other codes for furhter evaluation.2483

12.2 Status of inclusive calculations2484

12.2.1 Summary of existing calculations and implementations2485

Gluon fusion2486

Gluon fusion has been studied in great detail in the framework of the SM. In fact, the requirement2487

of higher order corrections to this process has been one of the most powerful driving forces for the2488

development of new theoretical concepts and techniques. The theory prediction currently used by the2489

experimental collaborations includes NNLO QCD corrections [140–142], resummation of soft-collinear2490

logarithms through NNLL [147], electro-weak effects [21, 25], and an estimate of the mixed QCD/EW2491

terms [151].2492

For the MSSM, however, the corrections to the gluon fusion process have been treated much less2493

rigorously until recently. Not even throughO(α3s), i.e. NLO QCD, has there been a prediction that2494

takes into account all strongly interacting SUSY particles. This is all the more remarkable, because the2495

technology for their calculation has been available since quite some time.2496

Schematically, the amplitude for Higgs production throughgluon fusion can be written as2497

A(gg → h) =∑

q∈{t,b}

(a(0)q + a

(0)q + a(1)q + a

(1)q + a

(1)qg

). (70)

The superscripts(0) and(1) denote one- and two-loop contributions, respectively. Theterma(0,1)q com-2498

prises contributions from Feynman diagrams with only the quark q and gluons running in loops. Sim-2499

29It should be noted that whileMSUSY formally is common for all three generations of scalar quarks, the only relevant onesare the third generation squarks. Consequently, limits obtained at the LHC on first and second generation squarks do not play arelevant role for this scenario.

November 18, 2011 – 11 : 26 DRAFT 125

ilarly, a(0,1)q contains only squarksq and gluons, whilea(1)qg is due to diagrams containing quarksq,2500

squarksq, and gluinos simultaneously.2501

Of course, also the real radiation of quarks and gluons has tobe taken into account:gg → hg,2502

qg → hq, andqq → hg. They are either quark- or squark-loop mediated, but no mixed quark/squark (or2503

gluino) terms occur at NLO.2504

The LO result,∑

q(a(0)q + a

(0)q ), has been known since a long time in analytic form. Also the2505

real radiation can be (and has been) evaluated quite straightforwardly using standard techniques, see2506

e.g. Refs. [63,139].2507

The pure quark termsa(0)q + a(1)q correspond to the NLO SM contribution. The first result that2508

was valid for a general quark to Higgs mass ratio was presented in Ref. [246, 247] in the form of one-2509

dimensional integrals. Meanwhile, more compact expressions in terms of analytic functions have been2510

found [136–138].2511

These general results justified with hindsight the use of theheavy-top limit for the gluon fusion2512

process within the Standard Model [62,135]: it approximates the exact QCD correction factorσNLO/σLO2513

to within 2-3% forMh < 2mt [248]. The question whether this observation carries over to NNLO has2514

been answered by comparing the asymptotic expansion of the total cross section in terms of1/mt to the2515

usually adopted expression2516

σeff =

(σNNLO

σLO

)

mt→∞

σLO(mt) . (71)

They agree at the sub-percent level [143, 145, 146, 249, 250]. It is thus fair to say that the SM-like2517

top-quark induced terms are known through NNLO, while the bottom quark terms are known through2518

NLO.2519

Technically, the squark-induced terms are very similar to the quark-induced ones. Consequently,2520

results for general squark masses are known also in this casethrough NLO [136, 138, 251]. In order to2521

arrive at a consistent result within the MSSM, also mixed quark/squark/gluino contributions need to be2522

taken into account, however.2523

For the top-sector, this has been done by constructing an effective Lagrangian where all SUSY2524

particles and the top quark are integrated out [252–254]. The SUSY effects are then reduced to the2525

calculation of the proper Wilson coefficient, while the actual process diagrams are identical to the ones2526

in the heavy-top limit in the SM case.2527

For the bottom-sector, this approach is no longer applicable in a straightforward way, because the2528

bottom quark cannot be assumed heavy. The problem are the mixed bottom/sbottom/gluino diagrams. A2529

numerical result for general masses has been presented in Ref. [255]. A more compact expresseion can be2530

obtained through asymptotic expansions in the limitmb,mg ≫MH,mb, as applied in Refs. [256,257].2531

In Ref. [257], all contributions of strongly interacting particles in the MSSM have been combined2532

in a single program. This includes (i) the exact real radiation contributions due to quark- and squark-loops2533

for both the top- and the bottom-sector; (ii) the exact two-loop virtual terms due to top- and bottom-quark2534

loops; (iii) the squark-loop and mixed quark/squark/gluino-induced terms in the limitMg = Mq1 =2535

Mq2 ≫ {MH,mt,mb}. Needless to say that this includes also all the interference terms.2536

The program linksFeynHiggs which provides the on-shell values of the input parameters.2537

b-Quark associated production2538

The inclusive total cross section for bottom-quark associated Higgs-boson production, denoted30 pp/pp →2539

(bb)H +X, can be calculated in two different schemes. As the mass of the bottom-quark is large com-2540

30The notation(bb)H is meant to indicate that thebb pair is not required as part of the signature in this process,so that itsfinal state momenta must be integrated over the full phase space.

November 18, 2011 – 11 : 26 DRAFT 126

pared to the QCD scale,mb ≫ ΛQCD, bottom-quark production is a perturbative process and canbe2541

calculated order by order. Thus, in a four-flavour scheme (4FS), where one does not considerb-quarks2542

as partons in the proton, the lowest-order QCD production processes are gluon-gluon fusion and quark-2543

antiquark annihilation,gg → bbH andqq → bbH, respectively. However, the inclusive cross section for2544

gg → (bb)H develops logarithms of the formln(µF/mb), which arise from the splitting of gluons into2545

nearly collinearbb pairs. The large factorization scaleµF ≈MH/4 corresponds to the upper limit of the2546

collinear region up to which factorization is valid [258–260]. For Higgs-boson massesMH ≫ 4mb, the2547

logarithms become large and spoil the convergence of the perturbative series. Theln(µF/mb) terms can2548

be summed to all orders in perturbation theory by introducing bottom parton densities. This defines the2549

so-called five-flavour scheme (5FS). The use of bottom distribution functions is based on the approxima-2550

tion that the outgoingb-quarks are at small transverse momentum. In this scheme, the LO process for2551

the inclusive(bb)H cross section is bottom fusion,bb → H.2552

If all orders in perturbation theory were taken into account, the four- and five-flavour schemes2553

would be identical, but the way of ordering the perturbativeexpansion is different. At any finite order,2554

the two schemes include different parts of the all-order result, and the cross section predictions do thus2555

not match exactly. While this leads to an ambiguity in the waythe cross section is calculated, it also offers2556

an opportunity to test the importance of various higher-order terms and the reliability of the theoretical2557

prediction. The 4FS calculation is available at NLO [261, 262], while the 5FS cross section has been2558

calculated at NNLO accuracy [263]. Electroweak corrections to the 5FS process have been found to be2559

small [264] and will not be considered in the numerical results presented here.2560

Theoretical uncertainties2561

→ R. Harlander, S. Heinemeyer, M. Spira, G. Weiglein2562

12.2.2 Santander matching2563

A simple and pragmatic formula for the combination of the four- and five-flavour scheme calculations2564

of bottom-quark associated Higgs-boson production has been suggested in Ref. [265]. The matching2565

formula originated from discussions among the authors of Ref. [265] at theHiggs Days at Santander2566

2009and is therefore dubbed “Santander matching”. We shall briefly describe the matching scheme and2567

provide matched predictions for the inclusive cross section pp→ (bb)H +X at the LHC operating at a2568

center-of-mass energy of 7 TeV.2569

The 4FS and 5FS calculations provide the unique descriptionof the cross section in the asymptotic2570

limits MH/mb → 1 andMH/mb → ∞, respectively. For phenomenologically relevant Higgs-boson2571

masses away from these asymptotic regions both schemes are applicable and include different types of2572

higher-order contributions. The matching suggested in Ref. [265] interpolates between the asymptotic2573

limits of very light and very heavy Higgs-bosons.2574

A comparison of the 4FS and 5FS calculations reveals that both are in numerical agreement for2575

moderate Higgs-boson masses (see Fig. 23 of Ref. [6]). Once larger Higgs-boson masses are considered,2576

the effect of the collinear logarithmsln(MH/mb) becomes more and more important and the two ap-2577

proaches begin to differ. The two approaches are combined insuch a way that they are given variable2578

weight, depending on the value of the Higgs-boson mass. The difference between the two approaches is2579

formally logarithmic. Therefore, the dependence of their relative importance on the Higgs-boson mass2580

should be controlled by a logarithmic term. The coefficientsare determined such that2581

(a) the 5FS gets 100% weight in the limitMH/mb → ∞ ;2582

(b) the 4FS gets 100% weight in the limit where the logarithmsare “small”. There is obviously quite2583

some arbitrariness in this statement. In Ref. [265] it is assumed that “small” meansln(MH/mb) =2584

2. The consequence of this particular choice is that the 4FS and the 5FS both get the same weight2585

November 18, 2011 – 11 : 26 DRAFT 127

for Higgs-boson masses around 100 GeV, consistent with the observed agreement between the 4FS2586

and the 5FS in this region.312587

This leads to the following formula2588

σmatched=σ4FS+ wσ5FS

1 + w, (72)

with the weightw defined as2589

w = lnMH

mb− 2 , (73)

andσ4FS andσ5FS denote the total inclusive cross section in the 4FS and the 5FS, respectively. For2590

mb = 4.75GeV and specific values ofMH, this leads to2591

σmatched∣∣MH=100GeV = 0.49σ4FS+ 0.51σ5FS,




σmatched∣∣MH=500GeV = 0.27σ4FS+ 0.73σ5FS.

(74)

A graphical representation of the weight factorw is shown in Fig. 63 (a).2592

The theoretical uncertainties in the 4FS and the 5FS calculations should be added linearly, using2593

the weightsw defined in Eq. (73). This ensures that the combined error is always larger than the minimum2594

of the two individual errors. Neglecting correlations and assuming equality of the uncertainties in the2595

4FS and 5FS calculations would imply that the matched uncertainty is reduced by a factor ofw/(1 +w)2596

with respect to the common individual uncertainties. This seems unreasonable. In the approach adopted2597

in Ref. [265] the matched uncertainty would be equal to the individual ones in this case. On the other2598

hand, taking the envelope of the 4FS and 5FS error bands seemsoverly conservative.2599

The theoretical uncertainties in the 4FS and the 5FS calculations are obtained throughµF-, µR-2600

, pdf-, andαs variation as described in Ref. [6]. They can be quite asymmetric, which is why the2601

combination should be done separately for the upper and the lower uncertainty limits:2602

∆σ± =∆σ4FS

± + w∆σ5FS±

1 + w, (75)

where∆σ4FS± and∆σ5FS

± are the upper/lower uncertainty limits of the 4FS and the 5FS, respectively.2603

We shall now discuss the numerical implications of the Santander matching and provide matched2604

predictions for the inclusive cross sectionpp → (bb)H +X at the LHC operating at a center-of-mass2605

energy of 7 TeV. The individual numerical results for the 4FSand 5FS calculations have been obtained2606

in the context of theLHC Higgs Cross Section Working Groupwith input parameters as described in2607

Ref. [6]. Note that the cross section predictions presentedbelow correspond to Standard Model bottom2608

Yukawa couplings and a bottom-quark mass ofmb = 4.75 GeV. SUSY effects can be taken into account2609

by simply rescaling the bottom Yukawa coupling to the propervalue [264,266].2610

Fig. 63 (b) shows the central values for the 4FS and the 5FS cross section, as well as the matched2611

result, as a function of the Higgs-boson mass. The ratio of the central 4FS and the 5FS predictions to2612

31Note that one should use thepole massfor mb here rather than the running mass, since it is really the dynamical mass thatrules the re-summed logarithms.

November 18, 2011 – 11 : 26 DRAFT 128

mH (GeV)

wei

ght w

0

0.5

1

1.5

2

2.5

3

100 150 200 250 300 350 400 450 50010

-1

1

10

10 2

100 150 200 250 300 350 400 450 500mH (GeV)

σ (f

b)

√s =7 TeV

4FS gg→bbH (NLO)

5FS bb→H (NNLO)

matched

µ=(2mb+mH)/4

MSTW2008

(a) (b)

Fig. 63: (a) Weight factorw, Eq. (73), as a function of the Higgs-boson massMH. The bottom-quarkpole mass has been set tomb = 4.75 GeV. (b) Central values for the total inclusive cross section in the4FS (red, dashed), the 5FS (green, dotted), and for the matched cross section (blue, solid). Here and inthe following we use the MSTW2008 pdf set [95] (NLO for the 4FS, NNLO for the 5FS).

10-1

1

10

10 2

100 150 200 250 300 350 400 450 500mH (GeV)

unce

rtai

nty

band

for

σ σ

±∆σ ±

(fb)

4FS gg→bbH (NLO)

5FS bb→H (NNLO)

matched

√s =7 TeV

µ=(2mb+mH)/4

MSTW2008

mH (GeV)

rela

tive

diffe

renc

es o

n σ

(σ4FS ± ∆σ± 4FS - σmatched) / σmatched

(σ5FS ± ∆σ± 5FS - σmatched) / σmatched

matched uncertainty

√s =7 TeV

µ=(2mb+mH)/4MSTW2008

-0.5

-0.4

-0.3

-0.2

-0.1

-0

0.1

0.2

0.3

0.4

0.5

100 150 200 250 300 350 400 450 500

(a) (b)

Fig. 64: (a) Theory uncertainty bands for the total inclusive cross section in the 4FS (red, dashed), the5FS (green, dotted), and for the matched cross section (blue, solid). (b) Uncertainty bands and centralvalues, relative to the central value of the matched result (same line coding as panel (a)).

the matched result is displayed in Fig. 64 (b) (central dashed and dotted line): forMH = 100 GeV,2613

the 4FS and the 5FS contribute with approximately the same weight to the matched cross section, with2614

deviations between the individual 4FS and the 5FS predictions and the matched one of less than 5%. With2615

increasing Higgs-boson mass, the 4FS result deviates more and more from the matched cross section due2616

to its decreasing weight. AtMH = 500 GeV, it agrees to less than 20% with the matched result, while2617

the 5FS is still within 8% of the latter.2618

The corresponding theory error estimates are shown in Fig. 64. The absolute numbers are dis-2619

played in panel (a), while in panel (b) they are shown relative to the central value of the matched result.2620

Up toMH ≈ 300 GeV, the combined uncertainty band covers the central values of both the 4FS and the2621

5FS. For larger Higgs-boson masses, the 4FS central value isslightly outside this band.2622

November 18, 2011 – 11 : 26 DRAFT 129

12.3 Status of differential cross sections2623

12.3.1 Dressing SM predictions with effective couplings2624

In making predictions for Higgs boson production (or decay)processes in the MSSM one has to face the2625

fact that certain types of higher-order corrections have only been calculated in the SM case up to now,2626

while their counterpart for the case of the MSSM is not yet available. One the one hand, starting from2627

dedicated MSSM calculations for Higgs cross sections or decay widths treats higher-order corrections of2628

SM-type and SUSY-type on the same footing. On the other hand,this approach may be lacking the known2629

to be relevant (or at least the most up to date) SM-type corrections. Consequently, it can be advantageous2630

to start from SM-type processes including all the known higher-order corrections, and to dress suitable2631

SM-calculation building blocks with appropriate MSSM coupling factors (effective couplings). At the2632

same time, for internal consistency, the MSSM prediction for Higgs boson masses etc. have to be used.2633

While for the results for the MSSM Higgs production in gluon fusion and in association with bottom2634

quarks we use a genuine MSSM calculation, for the weak boson fusion channel the genuine MSSM2635

result is compared to that of the effective coupling approach. A similar comparison for the other Higgs2636

production channels will be investigated in a later stage.2637

12.3.2 Implementation inPOWHEG of Higgs production via gluon fusion in the MSSM2638

The gluon-fusion mechanism,gg → φ (φ = h,H,A), is one of the most important processes for the2639

production of the neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM), where2640

the overview about the existing calculations is given in Section 12.2.1.2641

The aim is to obtain results for Higgs boson kinematic distributions, but going beyond the ap-2642

proximation of rescaling the quark contributions. The results are obtained by combining all the available2643

NLO-QCD information (including the superpartner contributions) with the description of initial-state2644

multiple gluon emission via a QCD parton shower (PS) Monte Carlo. The analysis relies on thePOWHEG2645

method [111, 112], which allows to systematically merge NLOcalculations with vetoed PS, avoiding2646

double counting and preserving the NLO accuracy in the totalcross section. The merging procedure can2647

be implemented using a computer code framework called thePOWHEG BOX [159], which allows to build2648

an event generator that always assigns a positive weight to the hardest event. ThePOWHEG implementation2649

of the gluon-fusion Higgs production process in the SM was reported in Ref. [104] (see also Ref. [267])2650

and subsequent modifications to include the finite quark masseffects were presented elsewhere [?].2651

We briefly summarize what is included in ourPOWHEG implementation ofgg → h,H in the MSSM2652

(with more details in Ref. [?].) For the contributions of diagrams with real-parton emission, as well as2653

for the leading-order (LO) virtual contributions, we use one-loop matrix elements with exact dependence2654

on the quark, squark and Higgs masses from Ref. [139]. Concerning the NLO-QCD virtual contributions2655

involving squarks, we use the results of Ref. [254] for the stop contributions, obtained in the approxima-2656

tion of vanishing Higgs mass, and the results of Ref. [256] for the sbottom contributions, obtained via2657

an asymptotic expansion in the large supersymmetric massesthat is valid up to and including terms of2658

O(m2b/m

2φ), O(mb/MSUSY) andO(M2

Z/M2SUSY), with MSUSY a generic superparticle mass. For the2659

remaining NLO-QCD contributions, arising from the two-loop diagrams with quarks and gluons, we use2660

the exact results of Ref. [138]. The two-loop electroweak corrections, for which a complete calculation2661

in the MSSM is not available, are included in an approximate way by properly rescaling the SM light-2662

quark contributions given in Refs. [21, 150]. This approximation is motivated by the observation that,2663

in the SM, the light-quark contributions make up the dominant part of the electroweak corrections when2664

the Higgs mass is below the threshold for top-pair production.2665

As discussed above, is necessary to compute the entire spectrum of masses and couplings of the2666

model in a consistent way, starting from a given set of input parameters. In our numerical analysis, we2667

use the codeSoftSusy [268] to compute the MSSM spectrum and the couplings of the Higgs bosons2668

to quarks and squarks starting from a set of running parameters expressed in theDR renormalization2669

November 18, 2011 – 11 : 26 DRAFT 130

scheme. However, it is in principle possible to interface our code with other spectrum calculators (such2670

as, e.g.,FeynHiggs) that adopt different choices of renormalization conditions for the input parameters.2671

For illustrative purposes we present numerical results forthe production of the lightest CP-even2672

Higgs boson,h, at the LHC with center-of-mass energy of 7 TeV, in a representative region of the2673

MSSM parameter space. Events are generated with our implementation ofPOWHEG, then matched with2674

thePYTHIA PS [126]. We compute the total inclusive cross section for light Higgs production in gluon2675

fusion, as well as the transverse momentum distribution fora light Higgs boson produced in association2676

with a jet, and we compare them with the corresponding quantities computed for a SM Higgs boson with2677

the same mass.2678

The relevant MSSM Lagrangian parameters are chosen as:2679

mQ = mU = mD = 500 GeV, Xt = 1250 GeV, M3 = 2M2 = 4M1 = 400 GeV, |µ| = 200 GeV,(76)

where:mQ, mU andmD are the soft SUSY-breaking mass terms for stop and sbottom squarks;Xt ≡2680

At − µ cot β is the left-right mixing term in the stop mass matrix, whereAt is the soft SUSY-breaking2681

Higgs-squark coupling andµ is the higgsino mass parameter in the superpotential;Mi (for i = 1, 2, 3)2682

are the soft SUSY-breaking gaugino masses. We consider the input parameters in Eq. (76) as expressed in2683

theDR renormalization scheme, at a reference scaleQ = 500 GeV. Our choice forXt corresponds to the2684

choice in themmaxh scenario. We recall that, in our conventions, thetan β-dependent corrections to the2685

relation between the bottom mass and the bottom Yukawa coupling [239] enhance the Higgs couplings2686

to bottom and sbottoms forµ < 0 and suppress them forµ > 0.2687

We perform a scan on the parameters that determine the Higgs boson masses and mixing at tree2688

level,MA andtan β, varying them in the ranges90 GeV ≤ MA ≤ 200 GeV and2 ≤ tan β ≤ 50.2689

For each value oftan β we deriveAt from the condition onXt, then we fix the corresponding Higgs-2690

sbottom coupling asAb = At. For each point in the parameter space, we useSoftSusy to compute the2691

physical (i.e., radiatively corrected) Higgs boson massesMh andMH, and the effective mixing angle2692

α that diagonalizes the radiatively corrected mass matrix inthe CP-even Higgs sector. We obtain from2693

SoftSusy also the MSSM running quark massesmt andmb, expressed in theDR scheme at the scale2694

Q = 500 GeV. The running quark masses are used both in the calculation of the running stop and2695

sbottom masses and mixing angles, and in the calculation of the top and bottom contributions to the2696

form factors for Higgs boson production (the latter are computed using theDR results presented in2697

Refs. [254,256]).2698

In Fig. 65 we plot the ratio of the cross section for the production of the lightest scalarh in the2699

MSSM over the cross section for the production of a SM Higgs boson with the same mass. For a2700

consistent comparison, we adopt theDR scheme in both the MSSM and the SM calculations. The plot2701

on the left is obtained withµ > 0, while the plot on the right is obtained withµ < 0. In order to2702

interpret the plots, it is useful to recall that for small values ofMA it is the heaviest scalarH that has2703

SM-like couplings to fermions, while the coupling ofh to top (bottom) quarks is suppressed (enhanced)2704

by tan β. In the lower-left region of the plots, with smallMA and moderatetan β, the enhancement of2705

the bottom contribution does not compensate for the suppression of the top contribution, and the MSSM2706

cross section is smaller than the corresponding SM cross section. On the other hand, for sufficiently2707

largetan β (in the lower-right region of the plots) the enhancement of the bottom contribution prevails,2708

and the MSSM cross section becomes larger than the corresponding SM cross section. Forµ < 0 the2709

coupling ofh to bottom quarks is further enhanced by thetan β-dependent threshold corrections, and the2710

ratio between the MSSM and SM predictions can significantly exceed a factor of ten. We also note that2711

for sufficiently largeMA, i.e. when the couplings ofh to quarks approach their SM values, the MSSM2712

cross section is smaller than the SM cross section.2713

To assess the genuine effect of the squark contributions (asopposed to the effect of the modifi-2714

cations in the Higgs-quark couplings), we plot in Fig. 66 theratio of the full MSSM cross section for2715

November 18, 2011 – 11 : 26 DRAFT 131

0.2

0.3

0.4 0.5

0.6

0.6

0.7

0.8

0.9

12

3

4

5

6

10 20 30 40 50

100

120

140

160

180

200

tanΒ

mAHG

eVL

0.2

0.3

0.4 0.5

0.6

0.60.7

0.80.9

1

2

3

4

56

7

8

9

10

20

30

40

50

60

70

10 20 30 40 50

100

120

140

160

180

200

tanΒ

mAHG

eVL

Fig. 65: Ratio of the total cross section forh production in the MSSM over the cross section for the production ofa SM Higgs boson with the same mass. The plot on the left is forµ > 0 while the plot on the right is forµ < 0.

0.7

0.75

0.8

0.85

0.90.95

1

10 20 30 40 50

100

120

140

160

180

200

tanΒ

mAHG

eVL

0.6

0.65

0.65

0.7

0.75

0.8

0.85 0.9

0.95

1

10 20 30 40 50

100

120

140

160

180

200

tanΒ

mAHG

eVL

Fig. 66: Ratio of the full cross section forh production in the MSSM over the approximated cross section computedwith only quarks running in the loops. The plot on the left is for µ > 0 while the plot on the right is forµ < 0.

the production of the lightest scalarh over the approximated MSSM cross section computed with only2716

quarks running in the loops. As in Fig. 65, the plot on the leftis obtained withµ > 0, while the plot2717

on the right is obtained withµ < 0. We observe that, in the considered region of the MSSM parameter2718

space, the squark contributions always reduce the total cross section. We identify three regions:i) for2719

sufficiently largetan β and sufficiently smallMA the squark contribution is modest, ranging between2720

−10% and zero; this region roughly coincides with the one in whichthe total MSSM cross section is2721

dominated by thetan β-enhanced bottom quark contribution, and is larger than theSM cross section;ii)2722

a transition region, where the corrections rapidly become as large as−30%; this region coincides with2723

the one in which the SM and MSSM cross sections are similar to each other;iii) for sufficiently large2724

November 18, 2011 – 11 : 26 DRAFT 132

MA the squark correction is almost constant, ranging between−40% and−30%; this region coincides2725

with the one in which the MSSM cross section is smaller than the corresponding SM cross section.2726

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 120 GeV , tanβ = 10 , mA = 200 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 120 GeV , tanβ = 10 , mA = 200 GeV

Fig. 67: Left: ratio of the transverse momentum distribution of the lightest scalarh in the MSSM over the trans-verse momentum distribution of a SM Higgs boson with the samemass. Right: ratio of the corresponding shapes.

We now discuss the distribution of the transverse momentumphT of a light scalarh produced in2727

association with a jet, considering two distinct scenarios. First, we take a point in the MSSM parameter2728

space (MA = 200 GeV, tan β = 10 andµ > 0) in which the coupling ofh to the bottom quark is not2729

particularly enhanced with respect to the SM value, so that the bottom contribution to the cross section is2730

not particularly relevant. Because a light Higgs boson cannot resolve the top and squark vertices, unless2731

we consider very large transverse momentum, we expect the form of thephT distribution to be very similar2732

to the one for a SM Higgs boson of equal mass, the two distributions just differing by a scaling factor2733

related to the total cross-section. This is illustrated in the left plot of Fig. 67, where we show the ratio of2734

the transverse momentum distribution forh over the distribution for a SM Higgs boson of equal mass. In2735

the right plot of Fig. 67 we show the ratio of the corresponding shapes, i.e. the distributions normalized2736

to the corresponding cross-sections. This ratio, as expected, is close to one in most of thephT range.2737

We then consider the opposite situation, namely when the coupling of h to the bottom quark is2738

significantly enhanced. In this situation two tree-level channels, i.e.bb → gh and bg → bh, can2739

also contribute to the production mechanism and influence the shape of thephT distribution [269, 270].2740

Leaving a study of the effects of those additional channels to a future analysis, we will now illustrate how2741

the kinematic distribution of the Higgs boson can help discriminate between the SM and the MSSM. To2742

this purpose, we focus on three points in the(MA, tan β) plane characterized by the fact that the total2743

cross section forh production agrees, within5%, with the cross section for the production of a SM2744

Higgs boson of equal mass. Thus, we are considering points around the curve labeled “1” in Fig. 652745

(we setµ < 0, as in the right plot of that figure). In the left panels of Fig.68 we show the ratio of2746

the transverse momentum distribution forh over the distribution for a SM Higgs boson of equal mass.2747

We see that, because of the enhancement of the bottom-quark contribution, the shape of the transverse2748

momentum distribution in the MSSM can differ significantly from the SM case. Indeed, the region2749

at smallphT can receive an enhancement (at moderatetan β) compared with the SM result, but also a2750

significant suppression (at largetan β). The tail at largephT can receive a suppression down to a factor 42751

(at moderatetan β), but can also almost coincide with the SM result (at largetan β).2752

In the right panels of Fig. 68, for the same points in the(MA, tan β) plane as in the left panels,2753

we show the ratio of thephT distribution over the approximate distribution computed with only quarks2754

running in the loops. Even though the light Higgs boson cannot resolve the squark loops, we see that the2755

squark contributions affect the shape of thephT distribution, because of the interference with the bottom2756

November 18, 2011 – 11 : 26 DRAFT 133

0

0.5

1

1.5

2 0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 114 GeV , tanβ = 20 , mA = 120 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 114 GeV , tanβ = 20 , mA = 120 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 118 GeV , tanβ = 24 , mA = 125 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 118 GeV , tanβ = 24 , mA = 125 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 122 GeV , tanβ = 44 , mA = 140 GeV

0

0.5

1

1.5

2

0 20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

R

pTh (GeV)

mh = 122 GeV , tanβ = 44 , mA = 140 GeV

Fig. 68: Left plots: ratio of the transverse momentum distribution for the lightest scalarh in the MSSM over thedistribution for a SM Higgs with the same mass. Right plots: ratio of the transverse momentum distribution forh in the MSSM over the approximate distribution computed withonly quarks running in the loops. The plots areobtained withµ < 0, and with three different choices ofMA andtanβ for which the MSSM and SM predictionsfor the total cross section agree within5%.

contribution. In particular, we observe that the squark contributions may yield an enhancement of the2757

distribution at smallphT , and in all cases they yield a negative correction forphT > 20 GeV. The negative2758

November 18, 2011 – 11 : 26 DRAFT 134

[GeV/c]T

Higgs p0 20 40 60 80100120140160180200220240

Eve

nts

/ 5 G

eV/c

1

10

210

310

410

510

[GeV/c]T

Higgs p0 20 40 60 80100120140160180200220240

Eve

nts

/ 5 G

eV/c

1

10

210

310

410

510 H →Pythia gg

Reweighted for b-loop

[GeV/c]T

Higgs p0 50 100 150 200 250 300

Eve

nts

/ 5 G

eV/c

1

10

210

310

410

510

[GeV/c]T

Higgs p0 50 100 150 200 250 300

Eve

nts

/ 5 G

eV/c

1

10

210

310

410

510 H →Pythia gg

Reweighted for b-loop

Fig. 69: GeneratedpHT distributions forMH = 140(400) GeV forgg → H process generated withPYTHIA (solid)and after re-weighting (dashed) to correct forgg → H production with onlyb-loop.

correction becomes quite flat, at about−40%, for phT > 100 GeV.2759

12.3.3 Difference in kinematic acceptance between SM and MSSM production ofgg → H → ττ2760

Current LHC MSSMH → ττ analyses [271, 272] use the Standard Model generation ofgg → H2761

events with the infinite top mass approximation as implemented in PYTHIA [126] (used by CMS) or2762

POWHEG [159] (used by ATLAS). Both ATLAS and CMS collaborations have presented analyses in2763

themmaxh scenario [273] as given in Eq. 69. At large values oftan β in themmax

h scenariogg → H2764

production proceeds predominantly via a bottom quark loop producing a softerpHT spectrum than that2765

predicted in the Standard Model production dominated by thetop loop [158, 274].32 As a result the2766

kinematic acceptance ofgg → H → ττ events is overestimated in the current LHC analyses. To2767

determine the size of this effect, thePYTHIA generatedpHT spectrum is re-weighted to match the shape2768

predicted when considering only theb-loop contribution to thegg → H process [158]. The efficiency of2769

H → ττ event selection in thee+ τ -jet final state in the CMS detector is then estimated before and after2770

re-weighting the events.2771

Samples ofgg → H → ττ events withMH = 140 GeV andMH = 400 GeV are generated2772

with PYTHIA using the infinite top mass approximation and theτ leptons are decayed withTAUOLA.2773

Using thepHT spectra obtained withb-loop only [158], the generated events are assigned weightswi =2774

Nb−loopi /N

Pythia

i in i bins ofpHT whereNPythia

i andNb−loopi are the normalized event rates expected2775

from PYTHIA and with onlyb-loop contribution respectively. Events withpHT < 240 GeV andpHT <2776

300 GeV are considered forMH = 140 GeV andMH = 400 GeV, respectively. Figure 69 shows the2777

generatedpHT distributions for the two mass points before and after applying the event weights.2778

The visible products ofτ lepton decays, electron andτ -jet (τh) are reconstructed and required2779

to pass kinematic selections as in the CMSH → ττ analysis [271]. The electron is required to have2780

pT > 20 GeV and|η| < 2.1 and theτh is required to havepT > 20 GeV and|η| < 2.3. Events2781

containing ae + τh pair separated by∆R > 0.5 are selected. The selection efficiency, defined as the2782

ratio of selected to generated events, is calculated beforeand after applying the reweighting procedure2783

32For tanβ ≥ 12 andMA = 140 GeV in themmaxh scenario the cross-section ofgg → φ (φ = h,H,A) production through

only b-loop [275] is less than 10% different from the full MSSMgg → φ production cross-section [6]

November 18, 2011 – 11 : 26 DRAFT 135

MH [GeV] Efficiency,PYTHIA gg → H Efficiency, re-weighted forb-loop Correction factor

140 0.073± 0.001 0.061± 0.001 0.84± 0.01400 0.165± 0.001 0.149± 0.001 0.90± 0.02

Table 43: Thee+ τh selection efficiencies before and after re-weighting to correct forb-loop contribution.

and shown in Table 43.2784

It is found that the efficiency for the MSSMgg → H → ττ process with only b-loop is smaller2785

than for the SMgg → H → ττ process by approximately 16% forMH = 140 GeV and 10% for2786

MH = 400 GeV. We thus conclude the difference is not negligible and should be taken into account in2787

the experimental analyses.2788

12.3.4 Higher-order MSSM corrections for WBF Higgs production2789

12.3.4.1 VBFNLO2790

Higgs production via vector boson fusion (VBF) is an important SM production channel at the LHC [8,2791

9,276]. In the MSSM, it is expected that at least one Higgs boson will have a significant coupling to the2792

weak bosons, meaning VBF should be an important production channel in the MSSM as well. Since the2793

latest release,VBFNLO [197, 198] has provided the ability to study production of the three neutral Higgs2794

bosonsh,H andA via vector boson fusion in the MSSM with real or complex parameters33.2795

The MSSM implementation makes use of the anomalous Higgs couplings previously available in2796

VBFNLO. These use the most general structure of the coupling between a scalar particle and a pair of2797

gauge bosons, which can be written as [199]2798

T µν(q1, q2) = a1(q1, q2)gµν + a2(q1, q2) [(q1q2) g

µν − qµ1 qν2 ] +

a3(q1, q2)ǫµνρσq1ρq2σ, (77)

wherea1,2,3 are Lorentz invariant formfactors andq1,2 are the momenta of the gauge bosons. Production2799

of the MSSM Higgs bosons is implemented inVBFNLO by altering the value of the formfactora1 (which2800

at tree-level is the only non-zero formfactor). The SM formfactor is altered by a SUSY factor for the2801

Higgs bosonsh andH as follows:2802

aSM1,HSMWW

=i eMW

sin θW, (78)

aMSSM1,hWW =

i eMW

sin θWsin(β − α), aMSSM

1,HWW =i eMW

sin θWcos(β − α). (79)

The MSSM parameters can be specified either via a SLHA file or, if VBFNLO is linked toFeynHiggs2803

[74–77], by the user.2804

12.3.4.2 Higgs mixing2805

Mixing between the neutral Higgs bosons can be extremely significant numerically34 , and needs to be2806

taken into account in order to produce phenomenologically relevant results. There is some flexibility,2807

however, in the manner in which this mixing is included in hteVBF process, andVBFNLO provides2808

several options. These are implemented by altering the formfactors of Eq. 79 appropriately, and are as2809

follows:2810

33At Born level in the MSSM with real parameters, the CP-odd Higgs bosonA is not produced.34In the MSSM with real parameters, mixing occurs between the two neutral CP-even Higgs bosons,h andH, and if complex

parameters are allowed, mixing between all three neutral Higgs bosons,h, H andA must be considered.

November 18, 2011 – 11 : 26 DRAFT 136

1. An effective Higgs mixing angle,αeff can be used (either the value ofαeff specified in the SLHA2811

file, or the effective angle output byFeynHiggs).2812

2. An improved Born approximation can be employed. In this case, the tree-level Higgs mixing angle2813

αtree is used and Higgs propagator factors (the Z-factors as defined in Ref. [77]) are applied to the2814

Born level Feynman diagrams as shown in Fig. 70(a). For this option, it is recommended that2815

FeynHiggs is used, which calculates the necessary Z-factors including all one-loop corrections as2816

well as the dominant two-loop corrections in the MSSM with complex parameters.352817

3. Since the Higgs mixing contributions are universal, the Z-factors can be applied not only at tree-2818

level but also at loop-level, as shown diagrammatically in Fig. 70(b). This option can have a2819

significant effect in more extreme regions of the MSSM parameter space, especially when CP-2820

violating effects are considered.2821

4. The Higgs mixing can be treated as, in effect, an additional counterterm that is added at NLO, as2822

shown in Fig. 70(c).2823

In themmaxh scenario, however, including mixing at loop-level as well as at tree-level has very2824

little effect, even in the non-decoupling regime.2825

Various Higgs decays are included inVBFNLO: H → γγ, H → µ+µ−, H → τ+τ−, H → bb,2826

H → W+W− → ℓ+νℓℓ−νℓ,H → ZZ → ℓ+ℓ−νℓνℓ andH → ZZ → ℓ+ℓ−ℓ+ℓ−. When working in the2827

MSSM, the branching ratios and widths needed can either be read from the SLHA file or taken from the2828

FeynHiggs output.2829

12.3.4.3 Electroweak corrections to VBF in the MSSM2830

In the SM, the electroweak corrections to VBF have been foundto be as important numerically as the2831

NLO QCD corrections –O(5%) in the mass range 100-200 GeV [193,196]. In the MSSM, these correc-2832

tions are also potentially important and should be considered for phenomenologically relevant studies.2833

In the decoupling region of the MSSM parameter space, these corrections tend to be – as expected – very2834

similar to those in the SM. In other areas of parameter space,however, the electroweak corrections can2835

differ significantly between the SM and the MSSM.2836

The dominant MSSM electroweak corrections to vector boson fusion can be calculated byVBFNLO,2837

involving self-energy, vertex, box and pentagon type diagrams, as described in Ref. [196], using code2838

generated with adapted versions ofFeynArts [279–283] andFormCalc [284, 285]. InVBFNLO, Higgs2839

boson vertex and self energy corrections are incorporated using an effectiveHVV vertex, with formfac-2840

tors as in Eq. 77, and an effectiveqqV coupling is used to include the loop corrections to that vertex. To2841

include the box and pentagon diagrams, the full2 → 3 matrix element is calculated.2842

In the SM, the full electroweak corrections to the t-channelVBF process are included. In the2843

MSSM all SM-type boxes and pentagons, together with all MSSMcorrections to the vertex and self2844

energy type diagrams can be calculated byVBFNLO. The remaining SUSY electroweak corrections – i.e.2845

the chargino and neutralino boxes and pentagons – have been studied using private code and are sub-2846

dominant in the investigatedmmaxh scenario. Due to this, and the large CPU-time needed to calculate2847

these corrections, they are not yet included inVBFNLO. The SUSY QCD corrections were investigated in2848

Ref. [13,286,287] and found to be small.2849

12.3.4.4 Renormalisation scheme2850

The structure of theHVV counterterms is different in the MSSM and the SM, as in the MSSM contribu-2851

tions from the off-diagonal Higgs field renormalisations and from the renormalisation oftan β must be2852

35If a SLHA file is used as input and this option is chosen,VBFNLO can calculate the Z-factors if linked toLoopTools [277,278], but only in the MSSM with real parameters, and only to one-loop level.

November 18, 2011 – 11 : 26 DRAFT 137

(a) Improved Born approximation (Higgs propagator corrections appliedat LO)

(b) Higgs propagator corrections applied at LO and NLO

(c) Higgs propagator corrections included as an additionalcounterterm

Fig. 70: Diagrammatic representation of methods of including Higgsmixing effects. These diagrams are for theproduction of the light CP-even Higgs,h, in the MSSM with real parameters – if complex parameters areallowed,additional diagrams must be included to account for mixing with the CP-odd Higgs bosonA.

included. The explicit form of the counterterms for theHWW vertices are given by2853

ΓCThWW =

ieMW

sin θWsin(β − α)

(δZe +

1

2

δM2W

M2W

+ δZWW +δ sin θWsin θW

+1

2δZhh

+sin β cos βcos(β − α)

sin(β − α)δ tan β

)+

1

2

ieMW

sin θWcos(β − α)δZHh

ΓCTHWW =

ieMW

cos θWcos(β − α)

(δZe +

1

2

δM2W

M2W

+ δZWW +δ sin θWsin θW

+1

2δZHH

− sin β cos βsin(β − α)

cos(β − α)δ tan β

)+

1

2

ieMW

sin θWsin(β − α)δZhH. (80)

November 18, 2011 – 11 : 26 DRAFT 138

A renormalisation scheme is used where the electroweak sector is renormalised on-shell, thus2854

ensuring that all renormalised masses of the gauge bosons correspond to the physical, measured masses2855

and their propagators’ poles are equal to 1. The Higgs fields,however, are renormalised using theDR2856

scheme, as described in Ref. [77].2857

VBFNLO offers several options for the parameterisation of the electromagnetic coupling. The choice2858

of parameterisation has a significant effect on the relativesize of the electroweak corrections, as the2859

charge renormalisation constant,δZe, must be altered to suit the LO coupling.2860

12.3.4.5 VBF parameters and cuts2861

The numerical results presented here were produced usingVBFNLO to simulate VBF production of the2862

light CP-even Higgs boson and have been evaluated in themmaxh scenario as described in Eq.??.2863

FeynHiggs-2.7.4 is used to calculate the MSSM parameters – in particular the Higgs boson2864

masses, mixing and widths. Matching the setup of the investigation of the vector boson fusion channel2865

in the SM, described in Section??, the electroweak parameters used here are as given in Appendix ??,2866

the electromagnetic coupling is defined via the Fermi constant GF, and the renormalization and factor-2867

izations scales are set toMW. The anti-kT algorithm is used to construct the jets, and the cuts used are2868

also as in Section??:2869

∆R = 0.5

pTj> 20 GeV

|yj | < 4.5

|yj1 − yj2 | > 4

mjj > 600 GeV. (81)

The Higgs boson is generated off shell.2870

For each parameter point the cross sections and distribution has been calculated twice – once in2871

the MSSM, inlcuding NLO QCD and all MSSM electroweak corrections except for the SUSY boxes2872

and pentagons (i.e. those containing charginos and neutralinos), and once in the SM with a Higgs mass2873

equal to that in the MSSM, including the complete SM QCD and electroweak corrections. The SM2874

cross section can then be rescaled by a SUSY factor, in order to assess the impact of the SUSY-type2875

corrections. Two SUSY factors have been investigated,SZ andSα, which can be expressed as follows:2876

SZ = |Zhh sin(β − αtree) + ZhH cos(β − αtree)|2

Sα = sin2(β − αeff). (82)

When working in the MSSM, the Improved Born Approximation has been used, as described in Sec-2877

tion 12.3.4.2.2878

12.3.4.6 Total cross sections2879

Table 44 shows the NLO cross sections (together with the statistical errors from the Monte Carlo inte-2880

gration) in the MSSM and for the rescaled SM with the MSTW2008NLO PDF set36. As expected, in the2881

decoupling regime (i.e. for large values ofMA), the rescaling of the SM works well, giving adjusted cross2882

sections within 2% of the true MSSM value. The rescaling is worst for high valuesof tan β and low2883

values ofMA, in the non-decoupling regime, where there is a factor of more than 3 difference between2884

the rescaled SM cross sections and the true MSSM cross section, implying that the SUSY corrections at2885

this point in parameter space are significant. It should be noted that in this region of parameter space the2886

36The simulation has also been run using the CTEQ6.6 PDF set, and very similar features were found.

November 18, 2011 – 11 : 26 DRAFT 139

leading order cross section is extremely small and the NLO corrections (particularly the electroweak con-2887

tributions) give rise to a K-factor of approximately 0.25, meaning that the “loop squared” terms would2888

also provide a significant contribution. For this scenario,there is not a large difference between the two2889

rescaling factors described in Eq. 82 –SZ performs slightly better in the more extreme regions of the2890

scenario (i.e. largetan β, smallMA), whereasSα provides a better description in the decoupling region.2891

In the SM, the electroweak corrections are of the order -10%.In the MSSM, the electroweak2892

corrections in the decoupling regime are slightly larger than this, by approximately 0.5-1%, and in the2893

non-decoupling regime the electroweak corrections becomemuch larger – more than -70% fortan β =2894

50 andMA = 100 GeV.2895

tanβ MA [GeV] NLO, MSSM [fb] NLO, SM×Sα [fb] NLO, SM×SZ [fb]

3100 148.261± 0.381 152.605± 0.298 153.425± 0.299200 249.060± 2.123 250.880± 1.548 252.419± 1.558500 253.411± 0.813 255.963± 0.698 257.394± 0.701

15100 13.059± 0.052 16.108± 0.024 16.066± 0.024200 236.179± 1.399 237.359± 1.392 238.746± 1.400500 235.097± 2.989 239.307± 0.899 240.668± 0.904

50100 0.544± 0.003 1.835± 0.007 1.806± 0.007200 237.742± 0.438 238.196± 0.597 239.551± 0.600500 236.179± 1.266 236.496± 2.518 237.832± 2.532

Table 44: Higgs NLO cross sections at 7 TeV with VBF cuts and the MSTW2008NLO PDF set, for themmaxh

scenario in the MSSM and for the corresponding SM cross section rescaled by the SUSY factorsSα andSZ , asdefined in Eq. 82.

12.3.4.7 Differential distributions2896

A number of differential distributions were generated for the parameter points above. Here, we examine2897

a selection of them for the two ’extreme’ points2898

tan β = 3,MA = 500 GeV

tan β = 50,MA = 100 GeV.

Each plot compares the leading order result in the MSSM (solid black) with the NLO MSSM value2899

(dotted green) and the SM NLO result rescaled by the SUSY factorsSα (pink dash-dotted) andSZ (red2900

short-dashed) using the MSTW2008NLO PDF set.2901

Figure 71 shows the azimuthal angle distribution,φjj between the two tagging jets. This distribu-2902

tion is of special interest in VBF studies, as it provides an opportunity to study the structure of theHVV2903

coupling. As with the total cross sections, for the low-tan β, high-MA case, the rescaling procedure2904

works reasonably well, but for the high-tan β, low-MA case (shown on the right-hand side of Fig. 71),2905

simply rescaling the SM cross section gives a very poor idea of the true MSSM result. It is important to2906

note, however, that shapes of the distributions are very similar at LO and NLO, in both the SM and the2907

MSSM, which means that the higher order corrections do not signifcantly alter the structure of theHVV2908

coupling.2909

November 18, 2011 – 11 : 26 DRAFT 140

LO - MSSMNLO - MSSM

ANLO - rescaled SM, S

ZNLO - rescaled SM, S

(fb)

jjφ ∆

/dσd

30

35

40

45

50

55

jjφ ∆

0 0.5 1 1.5 2 2.5 3

(a)

LO - MSSMNLO - MSSM



(fb)

jjφ ∆

/dσd

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

jjφ ∆

0 0.5 1 1.5 2 2.5 3

(b)

Fig. 71: Azimuthal angle distributions fortanβ = 3,MA = 500 GeV (left plot) andtanβ = 50,MA = 100 GeV(right plot), comparing the MSSM results with the rescaled SM values with the MSTW2008NLO PDF set.

Figure 72 presents the differential distribution of the transverse momentum of the leading jet (i.e.2910

the jet with the highestpT ). As with the azimuthal angle distribution, the SM rescaling is seen to work2911

well in the decoupling regime (left plot), but not in the non-decoupling regime (right plot), where the2912

MSSM electroweak corrections are much larger than in the SM.The shape, however, of the distribution2913

remains unchanged. The NLO corrections (and in particular the EW contribution) causes an increasing2914

reduction to the cross section at higher energy scales, as noted in Section??. This feature is exaggerated2915

in the MSSM, where the increase is greater.2916

The transverse momentum (pT,H) and rapidity (yH) differential distributions are shown in Fig-2917

ure 73, which shows the same general behaviour of the SM-MSSMcomparison as the previous plots.2918

The NLO corrections are much larger for the non-decoupling parameter point (right-hand plots), result-2919

ing in poorer rescaling behaviour, but the shape of the distributions is relatively unaffected. As with the2920

distribution of the transverse momentum of the leading jet,pT,j1, the magnitude of the NLO corrections2921

increases withpT , and increases at a greater rate in the MSSM withtan β = 50, MA = 100 GeV than2922

in the corresponding rescaled SM results. The NLO corrections to the Higgs rapidity distribution are2923

relatively constant as a function of the Higgs boson’s rapidity, although with hightan beta and lowMA,2924

the shape of the corrections is slightly more curved than in the MSSM, with smaller corrections at low2925

and high rapidities.2926

12.3.5 MSSM NLO corrections for Higgs radiation from bottomquarks in the 5FS2927

Apart from the total inclusive cross section for Higgs production at the LHC, it is important to have2928

predictions for (a) kinematical distributions of the Higgsboson and associated jets, and (b) the fraction2929

of events with zero, one, or more jets. In supersymmetric theories the associated production of a Higgs2930

boson with bottom quarks is the dominant process in a large parameter region of the MSSM (see, e.g.,2931

Ref. [6]). The proper theory description of this process hasbeen a subject of discussion for quite some2932

time. The result is a rather satisfactory reconciliation ofthe two possible approaches, the so-called four-2933

and five-flavor scheme (4FS and 5FS), which led to the “Santander-matching” procedure, see below.2934

November 18, 2011 – 11 : 26 DRAFT 141

LO - MSSMNLO - MSSM



(fb/

GeV

)T1j

/dp

σd

0

0.5

1

1.5

2

2.5

3

(GeV)T1j

p

0 50 100 150 200 250 300 350 400

(a)

LO - MSSMNLO - MSSM



(fb/

GeV

)T1j

/dp

σd

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

(GeV)T1j

p

0 50 100 150 200 250 300 350 400

(b)

Fig. 72: Transverse momentum of the leading jet fortanβ = 3, MA = 500 GeV (left plot) andtanβ = 50,MA = 100 GeV (right plot), comparing the MSSM results with the rescaled SM values with the MSTW2008NLOPDF set.

Higher order corrections in the 5FS are usually easier to calculate than in the 4FS, because one2935

deals with a2 → 1 rather than a2 → 3 process at LO. However, since the 5FS works in the collinear2936

approximation of the outgoing bottom quarks, effects from large transverse momenta of the bottom2937

quarks are taken into account only at higher orders in this approach. In fact, NNLO plays a special role2938

in the 5FS, which becomes obvious by noticing that it is the first order where the 5FS contains the LO2939

Feynman diagram of the 4FS [263]. Hence only then the 5FS includes two outgoing bottom quarks at2940

large transverse momentum.2941

With the total inclusive cross section under good theoretical control, it is natural to study more2942

differential quantities. Being a2 → 1 process, kinematical distributions in the 5FS are trivial at LO, just2943

like in gluon fusion: thepT of the Higgs boson vanishes, and the rapidity distribution is given by the2944

boost of the partonic relative to the hadronic system.2945

Non-trivial distributions require a jet in the final state. ThepT andy distributions of the Higgs2946

boson in the processbb → φ+jet were studied at NLO in Ref. [288] (here and in what follows, φ ∈2947

{h,H,A}). Combining these results with the NNLO inclusive total cross section [263], one may obtain2948

NNLO results with kinematical cuts.2949

As mentioned above, particularly interesting for experimental analyses is the decomposition of the2950

events intoφ + n-jet bins. The casen = 0 can be obtained at NNLO by calculating the casen ≥ 1 at2951

NLO level, and subtracting it from the total inclusive crosssection [289,290]. For consistency, however,2952

both ingredients should be evaluated using NNLO PDFs and running of αs. This is indicated by the2953

superscript NLO′ in the following equation:2954

σNNLOjet-veto ≡ σNNLO

0-jet = σNNLOtot − σNLO′

≥1-jet . (83)

Note that this equation is understood without any flavor requirements on the outgoing jet.2955

As an exemplary case, we consider results for the jet parameters (anti-kT [116])2956

R = 0.4 pjetT > 20 GeV, |ηjet| < 4.8 . (84)

November 18, 2011 – 11 : 26 DRAFT 142

LO - MSSMNLO - MSSM



(fb/

GeV

)TH

/dp

σd

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

(GeV)THp

0 50 100 150 200 250 300 350 400 450 500

(a)

LO - MSSMNLO - MSSM



(fb/

GeV

)TH

/dp

σd

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

(GeV)THp

0 50 100 150 200 250 300 350 400 450 500

(b)

LO - MSSMNLO - MSSM



(fb)

H/d

yσ

d

0

10

20

30

40

50

60

70

80

90

100

Hy

-5 -4 -3 -2 -1 0 1 2 3 4 5

(c)

LO - MSSMNLO - MSSM



(fb)

H/d

yσ

d

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Hy

-5 -4 -3 -2 -1 0 1 2 3 4 5

(d)

Fig. 73: Distribution of Higgs transverse momentum (upper plots) and rapidity (lower plots) fortanβ = 3,MA = 500 GeV (left plots) andtanβ = 50,MA = 100 GeV (right plots), comparing the MSSM results with therescaled SM values with the MSTW2008NLO PDF set.

Fig. 74 shows the contributions of the NNLO jet-vetoed (φ+ 0-jet) and the NLO inclusiveφ+jet rate to2957

the NNLO total cross section in themmaxh scenario for two different values oftan β. The corresponding2958

numbers are given in Tables 45 and 46. Note, however, that thesum of theφ + n-jet cross sections2959

does not add up exactly to the total rate, because they are evaluated at different perturbative orders, and2960

therefore with different sets of PDFs andαs evolution. These numbers have been derived from the SM2961

results of Ref. [290], reweighted by the MSSM bottom Yukawa coupling with the help ofFeynHiggs372962

Fig. 75 displays the relative perturbative errors, obtained by varying the renormalization scaleµR2963

37Thanks to Markus Warsinsky for providing us with these weight factors.

November 18, 2011 – 11 : 26 DRAFT 143

(a) (b)

(c) (d)

Fig. 74: Total in inclusive (solid/red) and Higgs plusn-jet cross section forn = 0 (dashed/blue) andn ≥ 1

(dotted/black) in themmaxh scenario for (a,b)tanβ = 5 and (c,d)tanβ = 30. Left and right column correspond to

the CP-even and the CP-odd Higgs bosons, respectively.

by a factor of two aroundµ0 =Mφ/4 while keeping the factorization scaleµF fixed atµ0, and then doing2964

the same withµF andµR interchanged. The PDF+αs uncertainties are those from MSTW2008 [95].2965

The full error was obtained by quadratically adding the perturbative to the PDF+αs error. Note that these2966

plots are the same as in the SM; the precise numerical values can therefore be taken from Ref. [290].2967

The 5FS has also been used in order to evaluate associatedφ+ b production through NLO [291],2968

which is contained in the recentφ+jet calculation [290]. Updated numbers can be obtained quite easily2969

with the help of the programMCFM [?]. Here, however, we use the program described in Ref. [290].2970

Employing again the NNLO result for the total inclusive cross section, one may evaluate theb-vetoed2971

cross section through NNLO, along the lines of Eq. (83):2972

σNNLOb-jet veto≡ σNNLO

0b = σNNLOtot − σNLO′

≥1b-jet . (85)

It should be recalled, however, that this quantity does not take into account the finiteb-jet efficiencyǫb.2973

This distinguishes it from the Higgs cross section with zerob-tagsσ0b-tag, which can be obtained by2974

November 18, 2011 – 11 : 26 DRAFT 144

(a) (b)

Fig. 75: Relative perturbative and full errors for (a) the jet-vetoed cross section and (b) the inclusiveφ+jet crosssection. The full error is obtained by adding the perturbative and the PDF+αs-error quadratically.

combiningσ0b with the rate for having one or twob quarks in the final state, i.e.,σ1b andσ2b [290]:2975

σNNLO0b-tag = σNNLO

0b + (1− ǫb)σNLO1b + (1− ǫb)

2σLO2b . (86)

In this case case, we set the jet parameters to2976

R = 0.4 , pbT > 20GeV, |ηb| < 2.5 . (87)

Theφ + 0b-, 1b-, and2b-contributions are shown, together with the total cross section, in Fig. 76, for2977

the same parameters as in Fig. 74. The numbers were again produced with the help of the results from2978

Ref. [290], reweighted by the corresponding MSSM Yukawa coupling.2979

12.3.6 MSSM NLO corrections for Higgs radiation from bottomquarks in the 4FS2980

→ M. Dittmaier, M. Krämer, M. Spira (4FS)2981

→ comparison?2982

12.3.7 Comparison of b-jet acceptance and kinematic distributions inbb → H production between2983

PYTHIA and high order calculations2984

At large values oftan β andMA thebb → φ (φ = h,H,A) process dominates the production of the2985

MSSM neutral Higgs bosons [292]. The most recent SUSYφ → ττ analysis in CMS [293] uses a2986

combination of two analyses: with at least one b-tagged jet and with zero b-tagged jets. For the event2987

generation ofpp → bbh process thePYTHIA Monte Carlo (process 186) is used. The comparison of2988

PYTHIA with the 4FS calculations is shown in the earlier paper [294] for thepT distribution ofb-jets2989

where good agreement at the level of 10 % is found. Here we compare acceptance efficiency forb-jets,2990

pT andη distributions forb-jets and Higgs bosons as given byPYTHIA with the high order calculations2991

in the 5FS described in Section??. The jets have been reconstructed from the final state partons using2992

the anti-kT algorithm with parameterR=0.5. The jet is defined as ab-jet if at least one b quark is present2993

in the list of the jet constituents. The kinematic acceptance cuts forb-jets used were the same as in the2994

CMS analysis [293]:pT > 20 GeV, |η| < 2.4. Tables 47 and 48 show the fraction ofb-jets within the2995

acceptance obtained from the high order calculations (second column) and fromPYTHIA generator (5-th2996

November 18, 2011 – 11 : 26 DRAFT 145

LHC @ 7 TeV, |yjet| < 4.8, pjetT > 20 GeV, R = 0.4; mmax

h (tan β = 5)

MA σNNLOtot [pb] σNNLO

0-jet [pb] σNLO≥1-jet [pb]

[GeV] A h H A h H A h H

100 8.42 9.84 0.392 4.43 5.38 0.180 4.03 4.59 0.214

110 6.12 7.10 0.574 3.09 3.74 0.261 3.05 3.40 0.315

120 4.54 5.05 0.788 2.22 2.59 0.353 2.35 2.47 0.436

130 3.43 3.54 0.974 1.62 1.78 0.429 1.83 1.77 0.545

140 2.63 2.48 1.07 1.19 1.23 0.461 1.44 1.26 0.606

150 2.04 1.78 1.06 0.894 0.878 0.446 1.14 0.913 0.611

160 1.60 1.33 0.974 0.681 0.652 0.400 0.924 0.686 0.573

170 1.27 1.03 0.861 0.522 0.505 0.344 0.749 0.536 0.516

180 1.02 0.836 0.744 0.406 0.407 0.291 0.613 0.434 0.453

190 0.825 0.698 0.635 0.320 0.339 0.242 0.503 0.364 0.392

200 0.673 0.599 0.539 0.254 0.290 0.201 0.417 0.313 0.337

210 0.552 0.526 0.457 0.203 0.254 0.165 0.348 0.275 0.290

220 0.457 0.470 0.387 0.163 0.227 0.136 0.292 0.246 0.249

230 0.380 0.427 0.328 0.133 0.206 0.113 0.246 0.224 0.213

240 0.318 0.393 0.278 0.108 0.190 0.0942 0.208 0.206 0.184

250 0.267 0.366 0.237 0.0894 0.176 0.0785 0.178 0.192 0.158

260 0.226 0.343 0.203 0.0735 0.165 0.0649 0.152 0.180 0.136

270 0.192 0.324 0.173 0.0600 0.156 0.0541 0.130 0.170 0.118

280 0.163 0.308 0.149 0.0509 0.148 0.0461 0.112 0.162 0.102

290 0.140 0.294 0.129 0.0426 0.142 0.0388 0.0967 0.155 0.0891

300 0.120 0.283 0.111 0.0363 0.136 0.0338 0.0836 0.149 0.0774

Table 45: Numerical values for the total cross sectionσNNLOtot , theφ + 0-jet rateσNNLO

0-jet , and the inclusiveφ+jetrateσNLO

≥1-jet for themmaxh scenario fortanβ = 5 (φ ∈ {h,H,A}).

column) forMH = 140 GeV and400 GeV. The errors of the theoretical calculations due to the scale2997

variation and PDF are shown in the third and fourth columns ofTables 47 and 48. The total theoretical2998

cross-section for the SMbb → H process forMH = 140 GeV is 0.108.85 pb and forMH = 400 GeV it2999

is 1.29 pb.3000

The good agreement betweenPYTHIA and the high order calculations in the 5FS is found for the3001

fractions of zerob-jets and at least oneb-jet in the acceptance. The fraction of twob-jets predicted by3002

the 5FS calculations is lower than given by PYTHIA, but agrees within the theoretical errors.3003

November 18, 2011 – 11 : 26 DRAFT 146

LHC @ 7 TeV, |yjet| < 4.8, pjetT > 20 GeV, R = 0.4; mmax

h (tan β = 30)

MA σNNLOtot [pb] σNNLO

0-jet [pb] σNLO≥1-jet [pb]

[GeV] A h H A h H A h H

100 259 265 0.776 136 140 0.365 124 127 0.415

110 188 195 1.93 94.9 98.4 0.906 93.8 97.0 1.03

120 140 141 7.19 68.2 68.9 3.38 72.3 72.7 3.85

130 105 64.2 46.0 49.7 30.6 21.4 56.3 34.0 24.8

140 80.8 11.1 71.2 36.6 5.25 32.2 44.3 5.92 39.2

150 62.7 3.83 59.8 27.5 1.81 26.2 35.2 2.04 33.6

160 49.3 2.03 48.0 20.9 0.955 20.4 28.4 1.08 27.7

170 39.1 1.32 38.4 16.1 0.621 15.8 23.0 0.702 22.6

180 31.4 0.961 30.9 12.5 0.453 12.3 18.9 0.513 18.6

190 25.4 0.756 25.1 9.86 0.356 9.74 15.5 0.404 15.3

200 20.7 0.625 20.5 7.81 0.295 7.74 12.8 0.334 12.7

210 17.0 0.535 16.9 6.26 0.252 6.20 10.7 0.286 10.6

220 14.0 0.471 13.9 5.01 0.222 4.97 8.98 0.252 8.92

230 11.7 0.423 11.6 4.08 0.200 4.05 7.56 0.226 7.51

240 9.77 0.386 9.71 3.33 0.182 3.31 6.41 0.206 6.37

250 8.22 0.357 8.17 2.75 0.168 2.73 5.46 0.191 5.43

260 6.95 0.334 6.91 2.26 0.157 2.25 4.66 0.178 4.64

270 5.90 0.315 5.87 1.85 0.148 1.84 3.99 0.168 3.97

280 5.03 0.299 5.00 1.57 0.141 1.56 3.44 0.160 3.43

290 4.30 0.286 4.28 1.31 0.135 1.30 2.97 0.153 2.96

300 3.70 0.274 3.68 1.12 0.129 1.11 2.57 0.146 2.56

Table 46: Same as Table 45, but fortanβ = 30.

final statei σthi /σthtot scale error(%) PDF error (%) PYTHIA pp → bbh

0 b-jet 0.6381 -14.4 +8.8 0.619oneb-jet 0.3286 -6.9 +4.4 0.325two b-jets 0.0417 -33.1 +59.0 0.056

Table 47: The fraction ofb-jets within the acceptance obtained from the high order calculations in the 5FS (secondcolumn) and fromPYTHIA generator (5-th column) forMH = 140 GeV. The errors of the theoretical calculationsdue to the scale variation and PDF in % are shown in third and fourth columns.

final statei σthi /σthtot scale error (%) PDF error (%) PYTHIA pp → bbh

0 b-jet 0.519 -7.2 +8.9 -6.7 +7.6 0.514oneb-jet 0.426 -8.9 +5.8 -6.4 +6.4 0.385two b-jets 0.063 -28.4 +45.5 -4.5 +4.4 0.101

Table 48: The fraction ofb-jets within the acceptance obtained from the high order calculations in the 5FS (secondcolumn) and fromPYTHIA generator (5-th column) forMH = 400 GeV. The errors of the theoretical calculationsdue to the scale variation and PDF are shown in thirth and fourth columns.

November 18, 2011 – 11 : 26 DRAFT 147

(a) (b)

(c) (d)

Fig. 76: Total inclusive (solid/red) and Higgs plusnb-jet cross section forn = 0 (dashed/blue),n = 1 (dot-ted/black), andn = 2 (dash-dotted/brown) in themmax

h scenario for (a,b)tanβ = 5 and (c,d)tanβ = 30. Leftand right column correspond to the CP-even and the CP-odd Higgs bosons, respectively.

November 18, 2011 – 11 : 26 DRAFT 148

13 Charged Higgs boson production383004

Many extensions of the Standard Model, in particular supersymmetric theories, require two Higgs dou-3005

blets leading to five physical scalar Higgs bosons, including two (mass-degenerate) charged particles3006

H±. The discovery of a charged Higgs boson would provide unambiguous evidence for an extended3007

Higgs sector beyond the Standard Model. Searches at LEP haveset a limitMH± > 79.3 GeV on the3008

mass of a charged Higgs boson in a general two-Higgs-doubletmodel [295]. One usually distinguishes3009

a “light charged Higgs”,MH± ≤ mt, and a “heavy charged Higgs”,MH± > mt. Within the MSSM,3010

the charged Higgs boson mass is constrained by the pseudoscalar Higgs mass and theW boson mass3011

throughM2H± =M2

A +M2W at tree level, with only moderate higher-order corrections[77,296–298]. A3012

mass limit on the MSSM charged Higgs boson can thus be derivedfrom the limit on the pseudoscalar3013

Higgs boson,MA > 93.4 GeV [245], resulting inMH±>∼ 120 GeV. At the Tevatron, searches for light3014

charged Higgs bosons in top-quark decayst → bH± [299, 300] have placed some constraints on the3015

MSSM parameter space, but do not provide any further genericbounds onMH±.3016

The main mechanism for light charged Higgs boson productionat the LHC is from decays of top3017

quarks intt events,t → H±b. There are two main mechanisms for charged Higgs boson production at3018

the LHC:3019

top-quark decay: t → bH±+X if MH±<∼ mt ,

associated production:pp → tbH±+X if MH±>∼ mt .

The first process is dominant for the light charged Higgs, while the second process dominates for a heavy3020

charged Higgs boson. Alternative production mechanisms like quark–antiquark annihilationqq′ → H±3021

andH± + jet production [301], associatedH±W∓ production [302], or Higgs pair production [303,3022

304] have suppressed rates, and it is not yet clear whether a signal could be established in any of those3023

channels. Some of the above production processes may, however, be enhanced in models with non-3024

minimal flavour violation. As the cross section for light charged Higgs boson production are significantly3025

higher than for heavy charged Higgs bosons, early searches at the LHC and also this section focuses3026

mainly on those. All results shown below are for themmaxh scenario of the MSSM.3027

13.1 Light charged Higgs boson3028

To estimate the cross section for events with charged Higgs bosons in top quark pair production, the3029

following ingredients are needed: The top quark pair production cross section, the branching ratio3030

BR(t → bH+) and the charged Higgs boson decay branching ratios. Complete scans of the (MH±, tan β)3031

plane for√s = 7 TeV are available in electronic format39.3032

13.1.1 Top quark pair production cross section3033

Thett production cross section at√s = 7 TeV is predicted to be165+4

−9 (scale)+7−7 (pdf) pb by approxi-3034

mate NNLO calculations [305, 306] recommended by the ATLAS Top Working Group [307]. The scale3035

uncertainty is obtained from a variation of the renormalization scale from 0.5 to 2 times its nominal3036

valueCHECK! . The pdf uncertainty obtained using MSTW2008 [95] is taken at the 68% C.L.; both3037

uncertainties should be added linearly.3038

13.1.2 Top quark decays via a charged Higgs boson3039

Some generic MSSM info to be removed by references to the neutral MSSM Higgs boson section once3040

ready3041

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx3042

The decay width calculation of the top quark to a light charged Higgs boson is compared for two3043

38M. Flechl, S. Heinemeyer, M. Krämer, S. Lehti (eds.); M. Hauru, M. Spira39https://twiki.cern.ch/twiki/bin/view/LHCPhysics/MSSMCharged

November 18, 2011 – 11 : 26 DRAFT 149

different programs, FEYNHIGGS, version 2.8.5 [74–77], and HDECAY, version 4.20 [14, 308].The3044

mmaxh benchmark scenario is used [7], which in the on-shell schemeis defined as3045

MSUSY = 1 TeV, Xt = 2MSUSY, µ = 200 GeV, Mg = 800 GeV, M2 = 200 GeV, Ab = At. (88)

In addition totan β andMH±, theµ parameter is varied with values±1000,±200 GeV [309]. The3046

Standard Model parameters are taken as given in Ref. [6], Appendix Table A.3047

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx3048

3049

TheFeynHiggs calculation is based on the evaluation ofΓ(t → W+b) andΓ(t → H+b). The3050

former is calculated at NLO according to Ref. [310]. The decay to the charged Higgs boson and the3051

bottom quark usesmt(mt) andmb(mt) in the Yukawa coupling, where the latter receives the additional3052

correction factor1/(1 + ∆b). The leading contribution to∆b is given by [243]3053

∆b =CF

2

αs

πmgµ tan β I(mb1

,mb2,mg) . (89)

Here,b1,2 are the sbottom mass eigenstates, andmg is the gluino mass. The numerical results presented3054

here are based on the evaluation of∆b in Ref. [311]. Furthermore additional QCD corrections taken3055

from Ref. [243] are included.3056

The codeHDECAY calculates the decay widths and branching ratios of the Higgs boson(s) in the SM3057

and the MSSM. For the SM it includes all kinematically allowed channels and all relevant higher-order3058

QCD corrections to decays into quark pairs and into gluons. TODO: HDECAY calculation description.3059

FeynHiggs has been run with the selected set of parameters. TheFeynHiggs output is then used3060

to set the values for theHDECAY input parameters. The main result from the comparison is shown in3061

Figs. 77 and 78. The decay widthΓ(t → W+b) calculated by both programs agrees very well, the3062

difference being only of the order of 0.2%. The difference inΓ(t → H+b) varies from negligible (0.1%)3063

to a maximum of about 9%, the largest difference being at highvalues oftan β, where differences in3064

the∆b evaluation are largest. A similarly good agreement is observed for the corresponding branching3065

ratio.3066

Figure 79 (left) shows the relative uncertainty of the totaldecay widthΓ(t → H+b), assuming3067

a residual uncertainties of the∆b corrections of 3% (which is reached after the inclusion of the lead-3068

ing two-loop contributions to∆b [83]. Combining the calculations ontt production and decay, the3069

cross section for the processpb → tt → WbH±b can be predicted. The result forσtt · BR(t →3070

bH±) · BR(t → bW±) · 2 at√s = 7 TeV is shown in Figure 79 (right), together with the dominating3071

systematic uncertainties: pdf and scale uncertainties on the tt cross section, 5% for missing one-loop3072

electro-weak diagrams, 2% for missing two-loop QCD diagrams, and∆b-induced uncertainties. The3073

theory uncertainties are added linearly to the (quadratically) combined experimental uncertainties.3074

13.1.3 Light charged Higgs boson decay3075

In themmaxh scenario of the MSSM, the BR(H± → τν) ≈ 1 for all parameter values still allowed by the3076

LEP experiments [295]. The uncertainty on this assumption is less than 1% and thus negligible compared3077

to other uncertainties.3078

The charged Higgs boson decay widths calculated withFeynHiggs andHDECAY inmmaxh benchmark3079

scenario are compared in the same manner as described in Section 13.1.2. The total decay width of the3080

charged Higgs boson is shown in Fig.80. The decay channelsH± → τντ , H± → AW, H± → cs,3081

H± → HW, H± → µνµ andH± → tb available in both programs are studied. ForH± → τντ ,3082

FeynHiggs includes, besides the Higgs propagator corrections up to the two-loop level also the full3083

one-loop vertex corrections. Concerning the latter, inHDECAY the pure electroweak one-loop corrections3084

are not included.HDECAY includes the full NLO QCD corrections to charged Higgs decays into quarks,3085

November 18, 2011 – 11 : 26 DRAFT 150

βtan0 10 20 30 40 50

)±bH

→(tΓ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

FeynHiggs

HDECAY

= -1000 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±Hm

= 160 GeV±Hm

LHC

HIG

GS

XS

WG

201

1

= 1

40 G

eV

±Hm

βtan0 10 20 30 40 50

)±bH

→(tΓ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

FeynHiggs

HDECAY

= -200 GeVµ

= 1

00 G

eV

±Hm = 1

20 G

eV

±Hm

= 160 GeV±Hm

LHC

HIG

GS

XS

WG

201

1

= 140 GeV

±Hm

βtan0 10 20 30 40 50

)±bH

→(tΓ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

FeynHiggs

HDECAY

= 200 GeVµ

= 100 GeV

±Hm

= 120 GeV

±Hm

= 160 GeV±Hm

LHC

HIG

GS

XS

WG

201

1

= 140 GeV±

Hm

βtan0 10 20 30 40 50

)±bH

→(tΓ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

FeynHiggs

HDECAY

= 1000 GeVµ

= 100 GeV

±Hm

= 120 GeV±

Hm

= 140 GeV±Hm

LHC

HIG

GS

XS

WG

201

1

= 160 GeV±Hm

Fig. 77: The decay widthΓ(t → bH±) calculated withFeynHiggs andHDECAY as a function oftanβ for differentvalues ofµ andMH±.

which are included inFeynHiggs only in the approximation of a heavy charged Higgs boson. The3086

experimentally most interesting decay channelH± → τντ showed a good agreement, withHDECAY con-3087

sistently predicting a 3.5% larger decay width thanFeynHiggs, due to the differences described above.3088

The result is shown in Fig.81. A good agreement is also found in theH± → µνµ channel, again with3089

HDECAY predicting consistently a∼ 3.5% larger decay width thanFeynHiggs. In theH± → cs channel3090

a notable discrepancy of 7-19% is found. The result of the comparison in theH± → cs channel is shown3091

in Fig. 82. The differences inH± → cs may be attributed to two sources: the QCD corrections imple-3092

mented inFeynHiggs are valid only in the limit of heavy charged Higgs masses (in comparison to the3093

quark masses), whereas inHDECAY they are more complete. Conversely, the evaluation of∆s, which is3094

crucial for the calculation ofΓ(H± → cs), is more complete inFeynHiggs. This channel can only play3095

a significant role for very low values oftan β, and is numerically negligible within themmaxh scenario.3096

13.2 Heavy charged Higgs boson3097

Some distributions... definitely for 4FS, hopefully also 5FS. Recommendation for matching a la San-3098

tander3099

November 18, 2011 – 11 : 26 DRAFT 151

βtan0 10 20 30 40 50

)±bH

→B

R(t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

FeynHiggs

HDECAY

= -1000 GeVµ

= 1

00 G

eV±

Hm

= 1

20 G

eV

±H

m

= 1

40 G

eV

±Hm

= 160 GeV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±bH

→B

R(t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

FeynHiggs

HDECAY

= -200 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±Hm

= 140 GeV

±Hm

= 160 GeV±

Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±bH

→B

R(t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

FeynHiggs

HDECAY

= 200 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±Hm

= 140 GeV

±Hm

= 160 GeV±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±bH

→B

R(t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

FeynHiggs

HDECAY

= 1000 GeVµ

= 100 G

eV

±Hm

= 120 GeV

±Hm

= 140 GeV

±Hm

= 160 GeV±Hm

LH

C H

IGG

S X

S W

G 2

011

Fig. 78: The branching fraction BR(t → bH±) calculated withFeynHiggs andHDECAY as a function oftanβ fordifferent values ofµ andMH±.

November 18, 2011 – 11 : 26 DRAFT 152

1 10 100tanβ

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

δΓ(t

->

H+ b)

mt(mt) = 166.8 GeV, mb(mt) = 2.31 GeV

∆b = -0.8

∆b = -0.2

∆b = +0.2

∆b = +0.8

100 110 120 130 140 150 160MH

± [GeV]

0

10

20

30

40

σ(pp

->

tt)

BR

(t -

> H

+ b) B

R(t

->

W+ b)

* 2

[pb]

mhmax

: mt(mt) = 166.8 GeV, mb(mt) = 2.31 GeV

tanβ = 5tanβ = 10tanβ = 30tanβ = 50

Fig. 79: Left: Relative uncertainty inΓ(t → bH±) assuming a 3% residual uncertainty in∆b. Right:σtt ·BR(t →bH±) ·BR(t → bW±) · 2 including scale and PDF uncertainties, uncertainties for missing electroweak and QCDcorrections, and∆b-induced uncertainties.

βtan0 10 20 30 40 50

)±(H

tota

lΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= -1000 GeVµ

= 100 GeV

±Hm

= 120 GeV

±Hm

= 140 GeV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±(H

tota

lΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= -200 GeVµ = 100 G

eV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±(H

tota

lΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= 200 GeVµ = 100 GeV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

)±(H

tota

lΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= 1000 GeVµ = 100 GeV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

Fig. 80: The decay width ofH± calculated withFeynHiggs andHDECAY as a function oftanβ for different valuesof µ andMH±.

November 18, 2011 – 11 : 26 DRAFT 153

βtan0 10 20 30 40 50

) τν τ → ±

(HΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= -1000 GeVµ

= 100 GeV

±Hm

= 120 GeV

±Hm

= 140 GeV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

) τν τ → ±

(HΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= -200 GeVµ = 100 G

eV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

) τν τ → ±

(HΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= 200 GeVµ = 100 GeV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

) τν τ → ±

(HΓ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FeynHiggs

HDECAY

= 1000 GeVµ = 100 GeV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

Fig. 81: The decay widthΓ(H± → τντ ) calculated withFeynHiggs andHDECAY as a function oftanβ fordifferent values ofµ andMH± .

βtan0 10 20 30 40 50

c s

)→±

(HΓ

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

FeynHiggs

HDECAY

= -1000 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±H

m =

140

GeV

±H

m =

160

GeV

±H

m

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

c s

)→±

(HΓ

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

FeynHiggs

HDECAY

= -200 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

c s

)→±

(HΓ

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

FeynHiggs

HDECAY

= 200 GeVµ

= 1

00 G

eV

±Hm

= 1

20 G

eV

±Hm

= 1

40 G

eV

±Hm

= 1

60 G

eV

±Hm

LH

C H

IGG

S X

S W

G 2

011

βtan0 10 20 30 40 50

c s

)→±

(HΓ

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

FeynHiggs

HDECAY

= 1000 GeVµ

= 100 GeV

±Hm

= 120 GeV

±Hm

= 140 GeV

±Hm

= 160 GeV

±Hm

LH

C H

IGG

S X

S W

G 2

011

Fig. 82: The decay widthΓ(H± → cs) calculated withFeynHiggs andHDECAY as a function oftanβ for differentvalues ofµ andMH± . A discrepancy of 7-19% is observed.

November 18, 2011 – 11 : 26 DRAFT 154

14 Predictions for Higgs production and decay with a 4th SM-like fermion generation3100

14.1 General setup3101

We study the extension of the SM that includes a 4th generation of heavy fermions, consisting of an up-and a down-type quark(t′,b′), a charged lepton(l′), and a massive neutrino(νl

′). The 4th-generationfermions all have the same coupling constants as their SM copies, but do not mix with the other threeSM generations. The masses of the hypothetical new fermionsin this study are

mb′ = ml′ = mνl′ = 600 GeV,

mt′ = mb′ +

[1 +

1

5ln

(MH

115 GeV

)]50 GeV, (90)

where the relation among them is used to escape current exclusion limits from electroweak (EW) preci-3102

sion data (see Refs. [312, 313]). In the following we call theStandard Model with3 generations “SM3”3103

and the Standard Model with a 4th generation of fermions “SM4”. Owing to screening (see below) LO3104

or NLO-QCD predictions typically depend only weakly on the precise values of masses of the heavy3105

fermions. This is completely different for NLO-EW corrections, which are enhanced by powers of the3106

masses of the heavy fermions and induce a strong dependence of the results on these masses.3107

14.2 Higgs production via gluon fusion3108

So far, the experimental analysis has concentrated on models with ultra-heavy 4th-generation fermions,3109

excluding the possibility that the Higgs boson decays to heavy neutrinos. Furthermore, the 2-loop EW3110

corrections have been included under the assumption that they are dominated by light fermions. At the3111

moment the experimental strategy consists in computing thecross-section ratioR = σ(SM4)/σ(SM3)3112

with HIGLU [308] while NLO EW radiative corrections are switched off.3113

In this section we concentrate on full 2-loop EW correctionsand refer to the work of Refs. [314,3114

315] for the inclusion of QCD corrections.3115

Let us consider the impact of 2-loop EW corrections to Higgs-boson production at LHC (through3116

gg fusion) in SM4. The naive expectation is that light fermionsdominate the low-Higgs-boson-mass3117

regime and, therefore, EW corrections can be well approximated by using the available ones [25, 26] in3118

SM3. It is worth noting that the leading behaviour of the EW corrections for high values of masses in the3119

4th generation has been known for a long time [316,317] (see also Ref. [318]) showing an enhancement3120

of radiative corrections.3121

To avoid misunderstandings we define the following terminology: for a given amplitudeA, in the3122

limit mf → ∞ we distinguishdecouplingfor A ∼ 1/m2f (or higher negative powers),screeningfor3123

A → constant (orA ∼ lnm2f ) andenhancementfor A ∼ m2

f (or higher positive powers). To discuss3124

decoupling we need few definitions: SM3 is the usual SM with one t−b doublet; SM4 is the extension3125

of SM3 with a new family of heavy fermions,t′−b′ andl′−νl′. All relevant formulae for the asymptotic3126

limit can be found in Refs. [316, 317]. Considering only EW corrections, the amplitude forgg fusion3127

reads403128

ASM3 = A1-loopt +ANLO

3 , ANLO3 = A2-loop

t + δFRt A1-loop

t ,

ASM4 = A1-loopQ +ANLO

4 , ANLO4 = A

2-loopQ + δFR

Q+LA1-loopQ , (91)

where3129

AQ = At+t′+b′, δFRQ+L

= δFR

t+t′+b′+l′+νl′ . (92)

40We here neglect the contributions ofb-quark loops which amount to about3%.

November 18, 2011 – 11 : 26 DRAFT 155

In Eq.(91)δFR gives the contribution from finite renormalization, including Higgs-boson wave-function3130

renormalization (see Sect.3.4 of Ref. [26] for technical details).3131

First we recall the standard argument for asymptotic behaviour in leading-order (LO)gg fusion,3132

extendible to next-to-leading (NLO) and next-to-next-to-leading (NNLO) QCD corrections [63], and3133

give a simple argument to prove enhancement at NLO EW level.3134

Any Feynman diagram contributing to the Higgs–gluon–gluonvertex has dimension one; however,3135

the totalHgg amplitude must be proportional toTµν = p1 · p2 δµν − p2µp1ν (wherep1,2 are the two3136

gluon momenta) because of gauge invariance. For any fermionf the Yukawa coupling is proportional3137

to mf/MW andT has dimension two; therefore, the asymptotic behaviour of any diagram must be3138

proportional toT/mf whenmf → ∞. The part of the diagram which is not proportional toT will3139

cancel in the total amplitude because of gauge invariance (all higher powers ofmf will go away, and3140

this explains the presence of huge cancellations in the total amplitude). At LO there is only one Yukawa3141

coupling as in NLO (NNLO) QCD where one adds only gluon lines,so there is screening. At EW NLO3142

there are diagrams with three Yukawa couplings, therefore giving the netm2f behaviour predicted in3143

Ref. [316], so there is enhancement and at 2-loop level it goes at most withm2f . To be more precise,3144

define3145

σSM3 (gg → H) = σLOSM3 (gg → H)(1+δ

(3)EW

), σSM4 (gg → H) = σLOSM4 (gg → H)

(1+δ

(4)EW

). (93)

Analysing the results of Refs. [316, 317], valid for a light Higgs boson, one can see that in SM3 there3146

is enhancement in the quark sector formt ≫ mb (δ(3)EW ∼ GFm2t , whereGF is the Fermi coupling3147

constant). The full calculation of Ref. [25] shows that the physical value for the top-quark mass is3148

not large enough to make this quadratic behaviour relevant with respect to the contribution from light3149

fermions. From Ref. [316] we can also understand that a hypothetical SM3 with degeneratet−b (mt =3150

mb = mq) would generate an enhancement in the small-Higgs-mass region with the opposite sign3151

(δ(3)EW ∼ −GFm2q). Moving to SM4, Eq. (62) of Ref. [317] shows that the enhanced terms coming from3152

finite renormalization exactly cancel the similar contribution from 2-loop diagrams formt′ = mb′, so3153

that for mass-degeneratet′−b′ (andmt ≫ mb) we observe screening in the 4th-generation quark sector.3154

This accidental cancellation follows from the3 of colourSU(3) and from the fact that we have3 heavy3155

quarks contributing to LO almost with the same rate (no enhancement at LO). However, the same is not3156

true forl′−νl′ (there are no 2-loop diagrams with leptons ingg fusion), so we observe enhancement in the3157

leptonic sector of SM4, which actually dominates the behaviour at small values ofMH. To summarize:3158

– SM3 with heavy–light quark doublet: (positive) enhancement;3159

– SM3 with heavy–heavy (mass-degenerate) quark doublet: (negative) enhancement;3160

– SM4 with heavy–light and heavy-heavy (mass-degenerate) quark doublets: enhancement in heavy–3161

light, screening in heavy–heavy;3162

– SM4 with heavy–heavyl′−νl′ doublet: enhancement.3163

We have verified that our (complete) results confirm the asymptotic estimates of Refs. [316,317].3164

In order to prove that light–fermion dominance in SM3 below300 GeV is a numerical accident3165

due to the fact that the top quark is not heavy enough, we have computedδ(3)EW for a top quark of800 GeV3166

atMH = 100 GeV and found top-quark dominance. A similar effect of the top-quarkt is also present in3167

SM4; if, for instance, we fix all heavy-fermion massesmf ′ to 600 GeV, we findδ(4)EW = 12.1%(29.1%)3168

atmt = 172.5 GeV(600 GeV).3169

Moving to SM4, the LOgg-fusion cross section is for a light Higgs boson about nine times the3170

one in SM3, e.g., see Ref. [319]; the contribution from pure 2-loop diagrams should have an impact three3171

times smaller than the equivalent one in SM3 in the small-MH region. Therefore, if one assumes that3172

also NLO SM4 is dominated by light-fermion corrections, i.e., that EW corrections are the same for SM33173

November 18, 2011 – 11 : 26 DRAFT 156

[GeV]HM100 200 300 400 500 600 700 800 900 1000

[%

]E

W4 δ

-70

-60

-50

-40

-30

-20

-10

0

10

20 WW ZZ tt

100 200 300 400

2

4

6

8

10

12

Fig. 83: Relative corrections in SM4 (t′−b′ andl′−νl′ doublets) due to 2-loop EW corrections togg → H. The

masses of the 4th-generation fermions are chosen accordingto Eq. (90). In the inset a blow-up of the small-MH

region is shown.

and SM4, one expectsδ(4)EW ≈ δ(4)EW/3 for very heavy fermions. According to Ref. [317] this would be3174

true provided that no heavy leptons are included.3175

The complete result (see Ref. [320]) is shown in Figure 83 where thet′−b′ and thel′−νl′ doublets3176

are included. Numbers for the relative EW corrections are listed in Table 49. Electroweak NLO cor-3177

rections due to the 4th generation are positive and large fora light Higgs boson, positive but relatively3178

small around thett threshold, and start to become negative around450 GeV. Increasing further the3179

value of the Higgs boson mass, the NLO effects tend to become huge and negative (δ(4)EW < −100%)3180

showing minima around the heavy-quark thresholds. Above those thresholdsδ(4)EW starts to grow again3181

and becomes positive aroundMH = 1750 GeV.3182

Having computed the EW correctionsδ(4)EW we should discuss some aspects of their inclusion in the3183

production cross sectionσ (gg → H+X), i.e. their interplay with QCD corrections and the remaining3184

theoretical uncertainty. The most accepted choice is givenby3185

σF = σLO(1 + δQCD

) (1 + δEW

), (94)

which assumes complete factorization of QCD and EW corrections. The latter is based on the work3186

of Ref. [151] where it is shown that, at zero Higgs momentum, exact factorization is violated but with a3187

negligible numerical impact; the result of Ref. [151] can beunderstood in terms of soft-gluon dominance.3188

The residual part beyond the soft-gluon-dominated part contributes up to5−10% to the total in-3189

clusive cross section (for every Higgs mass up to1 TeV). Thus, with EW corrections we are talking3190

about non-factorizable effects which are at most5% in SM4.3191

Furthermore, EW corrections become−100% just before the heavy-quark thresholds making3192

questionable the use of the perturbative approach. At EW NNLO there are diagrams with five Yukawa3193

couplings; according to our argument on decoupling the enhancement at 3 loops goes as the 4th power of3194

the heavy-fermion mass, unless some accidental screening will occur. Here we have no solid argument3195

to estimate the remaining uncertainty in the high-mass region and prefer to state that SM4 is in a fully3196

non-perturbative regime which should be approached with extreme caution. For the low-mass region3197

we can do no more than make educated guesses; therefore, assuming a leading 3-loop behaviour ofm4f ,3198

we estimate the remaining uncertainty to be of the order of(α/π)2(mf/MW)4 and thus1−2% in the3199

intervalMH = 100−150 GeV and almost negligible in the intermediate region, below600 GeV.3200

November 18, 2011 – 11 : 26 DRAFT 157

Table 49: NLO EW corrections togg → H+X cross sections in SM4 for the low-mass region:δ(4)EW ± ∆, where

∆ is the numerical integration error.

MH [GeV] δ(4)EW [%] ∆ [%] MH [GeV] δ

(4)EW [%] ∆ [%] MH [GeV] δ

(4)EW [%] ∆ [%]

100 12.283 0.005 181 8.351 0.006 346 2.361 0.048110 12.212 0.005 182 8.278 0.006 347 2.327 0.048120 12.118 0.005 183 8.286 0.008 348 2.356 0.048130 11.982 0.005 184 8.320 0.009 349 2.470 0.048140 11.780 0.005 185 8.336 0.009 350 2.570 0.019145 11.620 0.005 186 8.300 0.009 351 2.629 0.019150 11.394 0.005 187 8.246 0.007 353 2.721 0.020151 11.333 0.005 188 8.176 0.009 355 2.834 0.019152 11.265 0.005 189 8.107 0.010 360 3.049 0.048153 11.191 0.004 190 8.057 0.010 365 3.300 0.048154 11.099 0.004 195 7.757 0.010 370 3.405 0.048155 10.994 0.004 200 7.465 0.010 375 3.492 0.048156 10.862 0.004 210 7.044 0.010 380 3.589 0.049157 10.705 0.004 220 6.720 0.018 385 3.521 0.049158 10.510 0.004 230 6.399 0.019 390 3.463 0.048159 10.290 0.004 240 6.065 0.020 400 3.260 0.048160 10.112 0.004 250 5.815 0.019 410 3.020 0.047161 10.104 0.004 260 5.600 0.019 420 2.680 0.042162 10.202 0.004 270 5.273 0.020 430 2.211 0.037163 10.238 0.004 280 5.038 0.020 440 1.710 0.039164 10.197 0.004 290 4.795 0.019 450 1.139 0.039165 10.115 0.004 300 4.541 0.020 460 0.444 0.040166 10.019 0.005 310 4.349 0.019 470 -0.223 0.042167 9.919 0.005 320 4.106 0.020 480 -1.060 0.047168 9.822 0.005 325 3.978 0.020 490 -1.740 0.049169 9.726 0.005 330 3.847 0.020 500 -2.542 0.036170 9.632 0.005 335 3.688 0.020 550 -7.281 0.048171 9.531 0.005 336 3.663 0.049 600 -12.708 0.049172 9.432 0.005 337 3.589 0.049 650 -18.593 0.049173 9.334 0.005 338 3.539 0.048 700 -24.904 0.049174 9.234 0.005 339 3.463 0.047 750 -31.227 0.049175 9.134 0.005 340 3.417 0.049 800 -37.790 0.049176 9.027 0.005 341 3.317 0.049 850 -44.322 0.049177 8.907 0.005 342 3.223 0.049 900 -50.768 0.049178 8.786 0.005 343 3.169 0.049 950 -57.516 0.049179 8.639 0.005 344 3.048 0.049 1000 -64.187 0.045180 8.485 0.008 345 2.449 0.049

November 18, 2011 – 11 : 26 DRAFT 158

14.3 NLO corrections toH → 4f in SM43201

The results of theH → 4f decay channels have been obtained using the Monte Carlo generator3202

PROPHECY4F [15, 17, 321] which has been extended to support the SM4 model. PROPHECY4F can3203

calculate the EW and QCD NLO corrections to the partial widths for all 4f final states, i.e. leptonic,3204

semi-leptonic, and hadronic final states. Since the vector bosons are kept off shell, the results are valid3205

for Higgs masses below, near, and above the on-shell gauge-boson production thresholds. Moreover, all3206

interferences between WW and ZZ intermediate states are included at LO and NLO.3207

The additional corrections in the SM4 model arise from 4th-generation fermion loops in the3208

HWW/HZZ vertices, the gauge-boson self-energies, and the renormalization constants. For the large3209

4th-generation masses ofO(600 GeV) considered here the 4th-generation Yukawa couplings are large,3210

and the total corrections are dominated by the 4th-generation corrections. Numerically the NLO correc-3211

tions amount to about−85% and depend only weakly on the Higgs-boson mass, since the heavy-fermion3212

masses in the scenario of (90) have only a weak Higgs mass dependence. The corrections from the 4th3213

generation are taken into account at NLO with its full mass dependence, but their behaviour for large3214

masses can be approximated well by the dominant correctionsin the heavy-fermion limit. In this limit3215

the leading contribution can be absorbed into effective HWW/HZZ interactions in theGF renormaliza-3216

tion scheme,3217

LHV V =

√√2GFH

[2M2

WW†µW

µ(1 + δtotW ) +M2ZZµZ

µ(1 + δtotZ )]. (95)

The higher-order corrections are contained in the factorsδtotV whose expansion up to 2-loop order is given3218

by3219

δtot(1)V = δ(1)u + δ

(1)V , δ

tot(2)V = δ(2)u + δ

(2)V + δ(1)u δ

(1)V . (96)

The 1-loop expressions for a singleSU(2) doublet of heavy fermions with massesmA,mB are [322]3220

δ(1)u = NcXA

[7

6(1 + x) +

x

1− xlnx

], δ

(1)V = −2NcXA(1 + x), (97)

wherex = m2B/m

2A andXA = GFm

2A/(8

√2π2). The results for the 2-loop correctionsδtot(2)V can be3221

found in Ref. [323] for the QCD corrections ofO(αsGFm2f ′) and in Ref. [317] for the EW corrections3222

of O(G2Fm

4f ′). The correction to the partial decay width is then given by3223

ΓNLO ≈ ΓLO

[1 + δ

(1)Γ + δ

(2)Γ

]= ΓLO

[1 + 2δ

tot(1)V + (δ

tot(1)V )2 + 2δ

tot(2)V

]. (98)

The size of the 2-loop correctionsδ(2)Γ is about+15%, again depending only very weakly on3224

the Higgs mass. Due to the large 1-loop corrections PROPHECY4F includes the 2-loop QCD and EW3225

corrections in the heavy-fermion limit in addition to the exact 1-loop corrections.3226

The leading 2-loop terms can also be taken as an estimate of the error from unknown higher-order3227

corrections. This implies an error of 15% relative to the LO for the generic 4th-generation mass scale3228

mf ′ = 600 GeV on the partial width for allH → 4f decay channels. Assuming a scaling law of this3229

error proportional toX2A, the uncertainty is estimated to about100X2

A relative to the LO prediction.3230

However, since the correction grows large and negative, therelative uncertainty on the corrected width3231

gets enhanced to100X2A/(1 − 23XA + 100X2

A), where the linear term inXA parametrizes the 1-loop3232

correction and we have assumed a splitting as given in (90). Formf ′ = 600 GeV this results roughly in3233

an uncertainty of50% on the correctedH → 4f decay widths.3234

14.4 H → f f3235

The decay widths forH → f f are calculated with HDECAY [12–14] which includes the approximate3236

NLO and NNLO EW corrections for the decay channels into SM3 fermion pairs in the heavy SM43237

November 18, 2011 – 11 : 26 DRAFT 159

fermion limit according to Ref. [317] and NNLO EW/QCD corrections according to Ref. [323]. These3238

corrections originate from the wave-function renormalization of the Higgs boson and are thus universal3239

for all fermion species. The leading one-loop part is given by δ(1)u of Eq. (97). Numerically the 1-3240

loop correction to the partial decay widths into fermion pairs amounts to about +40%, while the 2-3241

loop correction contributes an additional +20%. The corrections are implemented as a factor assuming3242

them to factorize from whatever is included in HDECAY, sincethe approximate expressions emerge3243

as corrections to the effective Lagrangian after integrating out the heavy fermion species. The scale3244

of the strong couplingαs has been identified with the average mass of the heavy quarkst′,b′ of the3245

4th generation. Since the full SM4 two-loop corrections amount to about15−20% relative to the LO3246

result, and the NLO corrections amount to about+60%, the remaining theoretical uncertainties can be3247

estimated to be about 10% for the full partial decay widths into fermion pairs for the SM4 part, while the3248

uncertainties of the SM3 EW and QCD parts are negligible withrespect to that.3249

14.5 H → gg, γγ, γZ3250

For the decay modesH → gg, γγ, γZ, HDECAY [12–14] is used as well.3251

ForH → gg, HDECAY includes the NNNLO QCD corrections of the SM in the limit of a heavy3252

top quark [61–65], added to the heavy-quark loops, too. At NNLO the known mismatch between the3253

NNLO QCD corrections of the SM and of the SM4 [314, 315] is added. Since this mismatch is small3254

(less than 1%) it is assumed that the mismatch at NNNLO will benegligible, i.e. much smaller than3255

the residual QCD uncertainty of about 3%. In addition the full NLO EW corrections of Section 14.23256

have been included in factorized form, since the dominant part of the QCD corrections emerges from the3257

gluonic contributions on top of the corrections to the effective Lagrangian in the limit of heavy quarks,3258

while the mismatch emerges entirely from this effective Lagrangian [314,315]. Thus the total theoretical3259

uncertainties can be estimated to about 5%, where the missing quark mass dependence at NLO and3260

beyond is taken into account, too.3261

HDECAY [12–14] includes the full NLO QCD corrections to the decay modeH → γγ supple-3262

mented by the additional contributions of the 4th-generation quarks and charged leptons according to3263

Refs. [63,67,69].3264

Introduction of EW NLO corrections (two-loop level) to the decayH → γγ requires particular3265

attention. We write the amplitude as3266

A = ALO + λANLO + λ2ANNLO + . . . , λ =GFM

2W

8√2π2

. (99)

Part of the problem in including the NLO EW term is related to the fact that the cancellation between3267

theW and the fermion loops is stronger in the SM4 than in the SM3 so that the LO result is suppressed3268

more, by about a factor of2 on the level of the amplitude and thus a factor of4 at the level of the decay3269

width. Furthermore, the NLO corrections are strongly enhanced for ultra-heavy fermions in the fourth3270

generation; assuming a mass-degenerate scenario of600 GeV for the heavy fermions and a Higgs mass3271

of 100 GeV we get a correction to the decay width (interference of LOwith NLO) of −318%; clearly it3272

does not make sense and one should always remember that a badly behaving series should not be used3273

to fix limits on the parameters, i.e., on the heavy fermion masses, i.e., breakdown of perturbation thery3274

cannot be used to rescue the theory itself.3275

Extending the same techniques used forH → gg in Ref. [320] we have computed the exact3276

amplitude forH → γγ up to NLO order, EW only; assuming for simplicitymb′ = mt′ = mQ and3277

ml′ = mνl′ = mL (but the calculation gives results for any general setup) the amplitude can be written3278

as follows:3279

A = ALO

[1 + λ

(CQ

m2Q

M2W

+ CL

m2L

M2W

+R)], (100)

November 18, 2011 – 11 : 26 DRAFT 160

whereCQ,L andR depend on masses. In the asymptotic region,MH < 2MW ≪ mQ,mL we requireR3280

to be a constant and parametrize theC -functions as3281

CQ = − 192

5(1 + cQ τ) , CL = − 32

3(1 + cL τ) , (101)

wherecQ,L are also constant andτ = MH/(2MW). Note that forτ = R = 0 this is the leading two-3282

loop behavior predicted in Ref. [317] (see also Ref. [318] for the top-dependent contribution which we3283

hide here inR). By performing a fit to our exact result we obtain a good agreement in the asymptotic3284

region, showing that the additional corrections proportional toτ play a relevant role. For instance, with3285

fermions of the fourth generation heavier than300 GeV we have fit/exact−1 less than5% in the window3286

MH = [80−130] GeV.3287

The major part of the NLO corrections emerges from an effective Lagrangian in the heavy-particle3288

limit, therefore we should consider them as correction to the effective Feynman rules and thus to the3289

amplitude. As a result, we define NLO EW corrections toH → γγ as follows:3290

∣∣∣A∣∣∣2=∣∣∣ALO

∣∣∣2(1 + δEW) =

∣∣∣ALO + λANLO

∣∣∣2. (102)

This choice is also partially based on the fact that, due to the smallness of the LO amplitude, the interfer-3291

ence between LO and NNLO is expected to be suppressed as compared to the squared NLO amplitude.3292

To estimate the missing quartic corrections (in the heavy fermion masses) we assume a leading behavior3293

ofm4Q,m

4L for NNLO EW, i.e., no accidental cancellations. For a conservative estimate of the uncertainty3294

we use3295 ∣∣∣A∣∣∣2=∣∣∣ALO + λANLO

∣∣∣2± 2λ2

∣∣∣ALO

∣∣∣2 ∣∣∣CQ + CL

∣∣∣m4

f ′

M4W

, (103)

where we putmQ = mL = mf in the last term; given our setup the difference betweenmt′ andmb′3296

is irrelevant in estimating the uncertainty. Our educated guess has been to use the absolute value of the3297

NLO leading coefficient as the coefficient in the NNLO one. ForMH = 100 GeV andmf = 600 GeV3298

the corrections amount to−64.5% as compared to the−318% in the conventional (unrealistic) approach.3299

The effect of including NLO EW corrections is better discussed in terms of|ALO + ANLO|2;3300

this quantity decreases with increasing values ofMH and approaches zero aroundMH = 150 GeV3301

after which the effect is reversed. The reason for this behavior is due to the smallness ofALO due to3302

cancellations between bosonic and fermionic loops, whileANLO is relativley large, also due to absence3303

of the accidental cancellations as the ones observed in thegg channel. AroundMH = 150 GeV the3304

credibility of our estimate for the effect of the NNLO corrections becomes more questionable.3305

It is worth nothing that forH → V V the situation is different. There is no accidentally small LO3306

(there SM3=SM4 in LO) and the square ofANLO is taken into account by the leading NNLO term taken3307

from Ref. [317], giving the15% at NNLO, which serves as our error estimate.3308

The decay modeH → γZ is treated at LO only, since the NLO QCD corrections within the SM3309

are known to be small [73] and can thus safely be neglected. The EW corrections in the SM as well as3310

the SM4 are unknown. This implies a theoretical uncertaintyof the order of 100% in the intermediate3311

Higgs mass range within the SM4, since large cancellations between theW and fermion loops emerge at3312

LO similar to the decay modeH → γγ.3313


The results for the Higgs-boson production cross section via gluon fusion have been obtained by includ-3315

ing the NLO QCD corrections with full quark-mass dependence[63] and the NNLO QCD corrections3316

in the limit of heavy quarks [314, 315]. The full EW corrections [320] have been included in factorized3317

from as discussed in Section 14.2. We used the MSTW2008NNLO parton density functions [95] with3318

November 18, 2011 – 11 : 26 DRAFT 161

Table 50: SM4 Higgs-boson production cross section via gluon fusion including NNLO QCD and NLO EWcorrections using MSTW2008NNLO PDFs for

√s = 7 TeV.

MH [GeV] σ [pb] MH [GeV] σ [pb] MH [GeV] σ [pb] MH [GeV] σ [pb] MH [GeV] σ [pb]100 244 166 77.5 188 56.7 339 13.5 400 9.59110 199 167 76.3 189 56.0 340 13.5 410 8.80120 165 168 75.2 190 55.2 341 13.4 420 8.04130 138 169 74.1 195 51.8 342 13.3 430 7.33140 117 170 73.0 200 48.6 343 13.3 440 6.67145 107 171 71.9 210 43.0 344 13.2 450 6.05150 99.2 172 70.9 220 38.2 345 13.1 460 5.49151 97.6 173 69.9 230 34.2 346 13.1 470 4.98152 96.1 174 68.8 240 30.7 347 13.1 480 4.50153 94.6 175 67.9 250 27.7 348 13.1 490 4.08154 93.1 176 66.9 260 25.1 349 13.1 500 3.70155 91.7 177 65.9 270 22.8 350 13.1 550 2.26156 90.2 178 65.0 280 20.8 351 13.0 600 1.40157 88.7 179 64.0 290 19.1 352 13.0 650 0.875158 87.3 180 63.1 300 17.6 353 12.9 700 0.556159 85.8 181 62.2 310 16.3 354 12.9 750 0.360160 84.5 182 61.4 320 15.2 355 12.9 800 0.235161 83.3 183 60.6 330 14.2 360 12.6 850 0.156162 82.1 184 59.8 335 13.8 370 12.0 900 0.104163 81.0 185 59.0 336 13.8 375 11.6 950 0.0690164 79.8 186 58.3 337 13.7 380 11.2 1000 0.0456165 78.6 187 57.5 338 13.6 390 10.4

the strong coupling normalized toαs(MZ) = 0.11707 at NNLO. The results for the cross sections are3319

displayed in Table 50 for a centre-of-mass energy of√s = 7 TeV. The renormalization and factorization3320

scales have been chosen asµR = µF = MH/2. These numbers are larger by factors of 4–9 than the3321

corresponding SM cross sections. The QCD uncertainties areabout the same as in the SM case, while3322

the additional uncertainties due to the EW corrections havebeen discussed in Section 14.2.3323

The results for the Higgs branching fractions have been obtained in a similar way as those for3324

the results in SM3 in Refs. [6, 11]. While the partial widths for H → WW/ZZ have been computed3325

with PROPHECY4F, all other partial widths have been calculated with HDECAY.Then, the branching3326

ratios and the total width have been calculated from these partial widths. The full results of the Higgs3327

branching fractions for Higgs masses up to1 TeV are shown in Tables 51–52 for the 2-fermion final3328

states and in Tables 53–54 for the 2-gauge-boson final states. In the latter tables also the total Higgs3329

width is given. Tables 55–56 list the branching fractions for the e+e−e+e− ande+e−µ+µ− final states3330

as well as several combined channels. Apart from the sum of all 4-fermion final states (H → 4f ) the3331

results for all-leptonic final statesH → 4l with l = e, µ, τ, νe, νµ, ντ, the results for all-hadronic final states3332

H → 4q with q = u,d, c, s,b and the semi-leptonic final statesH → 2l2q are shown. To compare with3333

the pure SM3, Figure 84 shows the ratios between the SM4 and SM3 branching fractions for the most3334

important channels.3335

Results for NLO EW corrections to the decayH → γγ are shown in Table 57 for the window3336

[90−150]GeV. The effect on the branching fraction is shown in Table 58.3337

November 18, 2011 – 11 : 26 DRAFT 162

Table 51: SM4 Higgs branching fractions for 2-fermion decay channelsin the low- and intermediate-mass region.

MH [GeV] H → bb H → τ+τ− H → µ+µ− H → ss H → cc H → tt100 5.70 · 10−1 5.98 · 10−2 2.08 · 10−4 2.44 · 10−4 2.88 · 10−2 0.00110 5.30 · 10−1 5.67 · 10−2 1.97 · 10−4 2.26 · 10−4 2.68 · 10−2 0.00120 4.87 · 10−1 5.29 · 10−2 1.84 · 10−4 2.08 · 10−4 2.46 · 10−2 0.00130 4.36 · 10−1 4.82 · 10−2 1.67 · 10−4 1.86 · 10−4 2.20 · 10−2 0.00140 3.72 · 10−1 4.17 · 10−2 1.45 · 10−4 1.59 · 10−4 1.88 · 10−2 0.00145 3.33 · 10−1 3.75 · 10−2 1.30 · 10−4 1.42 · 10−4 1.68 · 10−2 0.00150 2.83 · 10−1 3.20 · 10−2 1.11 · 10−4 1.21 · 10−4 1.42 · 10−2 0.00151 2.71 · 10−1 3.08 · 10−2 1.07 · 10−4 1.16 · 10−4 1.37 · 10−2 0.00152 2.59 · 10−1 2.94 · 10−2 1.02 · 10−4 1.11 · 10−4 1.31 · 10−2 0.00153 2.46 · 10−1 2.80 · 10−2 9.70 · 10−5 1.05 · 10−4 1.24 · 10−2 0.00154 2.32 · 10−1 2.64 · 10−2 9.16 · 10−5 9.89 · 10−5 1.17 · 10−2 0.00155 2.17 · 10−1 2.47 · 10−2 8.57 · 10−5 9.24 · 10−5 1.09 · 10−2 0.00156 2.01 · 10−1 2.29 · 10−2 7.94 · 10−5 8.56 · 10−5 1.01 · 10−2 0.00157 1.83 · 10−1 2.09 · 10−2 7.25 · 10−5 7.80 · 10−5 9.22 · 10−3 0.00158 1.61 · 10−1 1.84 · 10−2 6.39 · 10−5 6.87 · 10−5 8.12 · 10−3 0.00159 1.38 · 10−1 1.58 · 10−2 5.49 · 10−5 5.90 · 10−5 6.97 · 10−3 0.00160 1.13 · 10−1 1.29 · 10−2 4.48 · 10−5 4.80 · 10−5 5.67 · 10−3 0.00161 8.91 · 10−2 1.02 · 10−2 3.55 · 10−5 3.80 · 10−5 4.49 · 10−3 0.00162 7.15 · 10−2 8.22 · 10−3 2.85 · 10−5 3.05 · 10−5 3.60 · 10−3 0.00163 6.00 · 10−2 6.91 · 10−3 2.40 · 10−5 2.56 · 10−5 3.02 · 10−3 0.00164 5.23 · 10−2 6.03 · 10−3 2.09 · 10−5 2.23 · 10−5 2.64 · 10−3 0.00165 4.68 · 10−2 5.39 · 10−3 1.87 · 10−5 1.99 · 10−5 2.36 · 10−3 0.00166 4.26 · 10−2 4.92 · 10−3 1.71 · 10−5 1.82 · 10−5 2.15 · 10−3 0.00167 3.94 · 10−2 4.55 · 10−3 1.58 · 10−5 1.68 · 10−5 1.98 · 10−3 0.00168 3.67 · 10−2 4.25 · 10−3 1.47 · 10−5 1.57 · 10−5 1.85 · 10−3 0.00169 3.45 · 10−2 4.00 · 10−3 1.39 · 10−5 1.47 · 10−5 1.74 · 10−3 0.00170 3.26 · 10−2 3.78 · 10−3 1.31 · 10−5 1.39 · 10−5 1.64 · 10−3 0.00171 3.10 · 10−2 3.60 · 10−3 1.25 · 10−5 1.32 · 10−5 1.56 · 10−3 0.00172 2.95 · 10−2 3.43 · 10−3 1.19 · 10−5 1.26 · 10−5 1.49 · 10−3 0.00173 2.83 · 10−2 3.29 · 10−3 1.14 · 10−5 1.20 · 10−5 1.42 · 10−3 0.00174 2.71 · 10−2 3.15 · 10−3 1.09 · 10−5 1.15 · 10−5 1.36 · 10−3 0.00175 2.60 · 10−2 3.03 · 10−3 1.05 · 10−5 1.11 · 10−5 1.31 · 10−3 0.00176 2.50 · 10−2 2.92 · 10−3 1.01 · 10−5 1.07 · 10−5 1.26 · 10−3 0.00177 2.41 · 10−2 2.81 · 10−3 9.75 · 10−6 1.03 · 10−5 1.21 · 10−3 0.00178 2.32 · 10−2 2.71 · 10−3 9.41 · 10−6 9.89 · 10−6 1.17 · 10−3 0.00179 2.23 · 10−2 2.62 · 10−3 9.07 · 10−6 9.52 · 10−6 1.13 · 10−3 0.00180 2.15 · 10−2 2.52 · 10−3 8.74 · 10−6 9.17 · 10−6 1.08 · 10−3 0.00181 2.06 · 10−2 2.42 · 10−3 8.40 · 10−6 8.80 · 10−6 1.04 · 10−3 0.00182 1.97 · 10−2 2.31 · 10−3 8.01 · 10−6 8.38 · 10−6 9.90 · 10−4 0.00183 1.86 · 10−2 2.19 · 10−3 7.60 · 10−6 7.95 · 10−6 9.38 · 10−4 0.00184 1.77 · 10−2 2.08 · 10−3 7.21 · 10−6 7.53 · 10−6 8.90 · 10−4 0.00185 1.68 · 10−2 1.98 · 10−3 6.87 · 10−6 7.17 · 10−6 8.47 · 10−4 0.00186 1.61 · 10−2 1.89 · 10−3 6.57 · 10−6 6.85 · 10−6 8.09 · 10−4 0.00187 1.54 · 10−2 1.82 · 10−3 6.31 · 10−6 6.57 · 10−6 7.76 · 10−4 0.00188 1.48 · 10−2 1.75 · 10−3 6.07 · 10−6 6.31 · 10−6 7.46 · 10−4 0.00189 1.43 · 10−2 1.69 · 10−3 5.86 · 10−6 6.09 · 10−6 7.20 · 10−4 0.00190 1.39 · 10−2 1.64 · 10−3 5.69 · 10−6 5.91 · 10−6 6.98 · 10−4 0.00195 1.20 · 10−2 1.43 · 10−3 4.94 · 10−6 5.10 · 10−6 6.03 · 10−4 0.00200 1.06 · 10−2 1.27 · 10−3 4.41 · 10−6 4.53 · 10−6 5.35 · 10−4 0.00210 8.71 · 10−3 1.05 · 10−3 3.64 · 10−6 3.71 · 10−6 4.38 · 10−4 0.00220 7.33 · 10−3 8.93 · 10−4 3.09 · 10−6 3.12 · 10−6 3.69 · 10−4 0.00

November 18, 2011 – 11 : 26 DRAFT 163

Table 52: SM4 Higgs branching fractions for 2-fermion decay channelsin the high-mass region.

MH [GeV] H → bb H → τ+τ− H → µ+µ− H → ss H → cc H → tt230 6.26 · 10−3 7.69 · 10−4 2.66 · 10−6 2.67 · 10−6 3.15 · 10−4 0.00240 5.42 · 10−3 6.71 · 10−4 2.33 · 10−6 2.31 · 10−6 2.73 · 10−4 0.00250 4.73 · 10−3 5.89 · 10−4 2.04 · 10−6 2.01 · 10−6 2.38 · 10−4 0.00260 4.17 · 10−3 5.24 · 10−4 1.82 · 10−6 1.78 · 10−6 2.10 · 10−4 2.40 · 10−7

270 3.71 · 10−3 4.69 · 10−4 1.62 · 10−6 1.58 · 10−6 1.86 · 10−4 1.07 · 10−5

280 3.32 · 10−3 4.23 · 10−4 1.47 · 10−6 1.41 · 10−6 1.67 · 10−4 5.13 · 10−5

290 2.99 · 10−3 3.82 · 10−4 1.33 · 10−6 1.27 · 10−6 1.50 · 10−4 1.45 · 10−4

300 2.70 · 10−3 3.48 · 10−4 1.21 · 10−6 1.15 · 10−6 1.36 · 10−4 3.26 · 10−4

310 2.47 · 10−3 3.20 · 10−4 1.11 · 10−6 1.05 · 10−6 1.24 · 10−4 6.60 · 10−4

320 2.26 · 10−3 2.94 · 10−4 1.02 · 10−6 9.61 · 10−7 1.13 · 10−4 1.28 · 10−3

330 2.07 · 10−3 2.72 · 10−4 9.41 · 10−7 8.83 · 10−7 1.04 · 10−4 2.52 · 10−3

335 1.99 · 10−3 2.62 · 10−4 9.07 · 10−7 8.48 · 10−7 1.00 · 10−4 3.68 · 10−3

336 1.98 · 10−3 2.60 · 10−4 9.00 · 10−7 8.42 · 10−7 9.94 · 10−5 4.00 · 10−3

337 1.96 · 10−3 2.58 · 10−4 8.94 · 10−7 8.36 · 10−7 9.86 · 10−5 4.36 · 10−3

338 1.95 · 10−3 2.56 · 10−4 8.88 · 10−7 8.30 · 10−7 9.79 · 10−5 4.78 · 10−3

339 1.93 · 10−3 2.54 · 10−4 8.82 · 10−7 8.23 · 10−7 9.72 · 10−5 5.26 · 10−3

340 1.92 · 10−3 2.53 · 10−4 8.76 · 10−7 8.18 · 10−7 9.64 · 10−5 5.83 · 10−3

345 1.85 · 10−3 2.45 · 10−4 8.48 · 10−7 7.89 · 10−7 9.31 · 10−5 1.60 · 10−2

346 1.83 · 10−3 2.42 · 10−4 8.38 · 10−7 7.79 · 10−7 9.19 · 10−5 2.21 · 10−2

347 1.80 · 10−3 2.38 · 10−4 8.24 · 10−7 7.65 · 10−7 9.03 · 10−5 3.08 · 10−2

348 1.76 · 10−3 2.33 · 10−4 8.07 · 10−7 7.49 · 10−7 8.85 · 10−5 4.23 · 10−2

349 1.72 · 10−3 2.27 · 10−4 7.87 · 10−7 7.31 · 10−7 8.63 · 10−5 5.66 · 10−2

350 1.67 · 10−3 2.21 · 10−4 7.67 · 10−7 7.12 · 10−7 8.40 · 10−5 7.25 · 10−2

351 1.63 · 10−3 2.16 · 10−4 7.47 · 10−7 6.93 · 10−7 8.18 · 10−5 8.78 · 10−2

352 1.59 · 10−3 2.10 · 10−4 7.29 · 10−7 6.76 · 10−7 7.98 · 10−5 1.03 · 10−1

353 1.55 · 10−3 2.05 · 10−4 7.11 · 10−7 6.59 · 10−7 7.77 · 10−5 1.18 · 10−1

354 1.51 · 10−3 2.00 · 10−4 6.93 · 10−7 6.42 · 10−7 7.57 · 10−5 1.32 · 10−1

355 1.47 · 10−3 1.95 · 10−4 6.75 · 10−7 6.25 · 10−7 7.38 · 10−5 1.46 · 10−1

360 1.29 · 10−3 1.72 · 10−4 5.97 · 10−7 5.51 · 10−7 6.50 · 10−5 2.09 · 10−1

370 1.03 · 10−3 1.38 · 10−4 4.79 · 10−7 4.41 · 10−7 5.20 · 10−5 3.05 · 10−1

375 9.38 · 10−4 1.26 · 10−4 4.35 · 10−7 3.99 · 10−7 4.71 · 10−5 3.41 · 10−1

380 8.57 · 10−4 1.15 · 10−4 3.99 · 10−7 3.65 · 10−7 4.30 · 10−5 3.71 · 10−1

390 7.31 · 10−4 9.85 · 10−5 3.42 · 10−7 3.11 · 10−7 3.67 · 10−5 4.18 · 10−1

400 6.38 · 10−4 8.63 · 10−5 2.99 · 10−7 2.71 · 10−7 3.20 · 10−5 4.50 · 10−1

410 5.66 · 10−4 7.69 · 10−5 2.67 · 10−7 2.41 · 10−7 2.84 · 10−5 4.73 · 10−1

420 5.09 · 10−4 6.96 · 10−5 2.41 · 10−7 2.17 · 10−7 2.56 · 10−5 4.90 · 10−1

430 4.65 · 10−4 6.37 · 10−5 2.21 · 10−7 1.98 · 10−7 2.33 · 10−5 5.03 · 10−1

440 4.28 · 10−4 5.88 · 10−5 2.04 · 10−7 1.82 · 10−7 2.15 · 10−5 5.11 · 10−1

450 3.97 · 10−4 5.48 · 10−5 1.90 · 10−7 1.69 · 10−7 1.99 · 10−5 5.17 · 10−1

460 3.70 · 10−4 5.14 · 10−5 1.78 · 10−7 1.58 · 10−7 1.86 · 10−5 5.21 · 10−1

470 3.48 · 10−4 4.84 · 10−5 1.68 · 10−7 1.48 · 10−7 1.75 · 10−5 5.24 · 10−1

480 3.28 · 10−4 4.58 · 10−5 1.59 · 10−7 1.40 · 10−7 1.65 · 10−5 5.24 · 10−1

490 3.11 · 10−4 4.36 · 10−5 1.51 · 10−7 1.32 · 10−7 1.56 · 10−5 5.24 · 10−1

500 2.96 · 10−4 4.16 · 10−5 1.44 · 10−7 1.26 · 10−7 1.48 · 10−5 5.22 · 10−1

550 2.39 · 10−4 3.41 · 10−5 1.18 · 10−7 1.02 · 10−7 1.20 · 10−5 5.07 · 10−1

600 2.02 · 10−4 2.92 · 10−5 1.01 · 10−7 8.58 · 10−8 1.01 · 10−5 4.82 · 10−1

650 1.74 · 10−4 2.55 · 10−5 8.84 · 10−8 7.39 · 10−8 8.72 · 10−6 4.52 · 10−1

700 1.52 · 10−4 2.26 · 10−5 7.82 · 10−8 6.46 · 10−8 7.61 · 10−6 4.21 · 10−1

750 1.34 · 10−4 2.01 · 10−5 6.97 · 10−8 5.68 · 10−8 6.69 · 10−6 3.88 · 10−1

800 1.18 · 10−4 1.80 · 10−5 6.24 · 10−8 5.02 · 10−8 5.91 · 10−6 3.56 · 10−1

1000 7.37 · 10−5 1.17 · 10−5 4.06 · 10−8 3.13 · 10−8 3.69 · 10−6 2.43 · 10−1

November 18, 2011 – 11 : 26 DRAFT 164

Table 53: SM4 Higgs branching fractions for 2-gauge-boson decay channels and total Higgs width in the low- andintermediate-mass region.

MH [GeV] H → gg H → γγ H → Zγ H → WW H → ZZ ΓH [GeV]100 3.39 · 10−1 1.31 · 10−4 1.70 · 10−5 1.67 · 10−3 1.35 · 10−4 5.52 · 10−3

110 3.78 · 10−1 1.72 · 10−4 1.35 · 10−4 7.20 · 10−3 5.83 · 10−4 6.41 · 10−3

120 4.10 · 10−1 2.26 · 10−4 4.06 · 10−4 2.27 · 10−2 2.37 · 10−3 7.49 · 10−3

130 4.28 · 10−1 2.95 · 10−4 8.51 · 10−4 5.77 · 10−2 7.12 · 10−3 8.92 · 10−3

140 4.20 · 10−1 3.81 · 10−4 1.46 · 10−3 1.29 · 10−1 1.68 · 10−2 1.11 · 10−2

145 4.01 · 10−1 4.29 · 10−4 1.80 · 10−3 1.86 · 10−1 2.36 · 10−2 1.28 · 10−2

150 3.63 · 10−1 4.74 · 10−4 2.13 · 10−3 2.75 · 10−1 3.09 · 10−2 1.55 · 10−2

151 3.53 · 10−1 4.82 · 10−4 2.19 · 10−3 2.97 · 10−1 3.23 · 10−2 1.62 · 10−2

152 3.41 · 10−1 4.89 · 10−4 2.24 · 10−3 3.21 · 10−1 3.35 · 10−2 1.71 · 10−2

153 3.28 · 10−1 4.95 · 10−4 2.29 · 10−3 3.48 · 10−1 3.46 · 10−2 1.81 · 10−2

154 3.13 · 10−1 4.99 · 10−4 2.32 · 10−3 3.78 · 10−1 3.54 · 10−2 1.93 · 10−2

155 2.96 · 10−1 5.00 · 10−4 2.34 · 10−3 4.12 · 10−1 3.59 · 10−2 2.08 · 10−2

156 2.77 · 10−1 5.00 · 10−4 2.34 · 10−3 4.52 · 10−1 3.59 · 10−2 2.25 · 10−2

157 2.55 · 10−1 4.96 · 10−4 2.33 · 10−3 4.94 · 10−1 3.55 · 10−2 2.48 · 10−2

158 2.27 · 10−1 4.80 · 10−4 2.25 · 10−3 5.49 · 10−1 3.39 · 10−2 2.84 · 10−2

159 1.97 · 10−1 4.61 · 10−4 2.15 · 10−3 6.09 · 10−1 3.15 · 10−2 3.32 · 10−2

160 1.62 · 10−1 4.35 · 10−4 2.01 · 10−3 6.80 · 10−1 2.78 · 10−2 4.10 · 10−2

161 1.30 · 10−1 4.49 · 10−4 2.01 · 10−3 7.41 · 10−1 2.40 · 10−2 5.21 · 10−2

162 1.06 · 10−1 3.65 · 10−4 1.65 · 10−3 7.89 · 10−1 2.11 · 10−2 6.52 · 10−2

163 8.98 · 10−2 3.11 · 10−4 1.42 · 10−3 8.19 · 10−1 1.93 · 10−2 7.81 · 10−2

164 7.92 · 10−2 2.74 · 10−4 1.27 · 10−3 8.41 · 10−1 1.84 · 10−2 9.01 · 10−2

165 7.15 · 10−2 2.48 · 10−4 1.16 · 10−3 8.56 · 10−1 1.80 · 10−2 1.01 · 10−1

166 6.59 · 10−2 2.29 · 10−4 1.08 · 10−3 8.66 · 10−1 1.80 · 10−2 1.12 · 10−1

167 6.16 · 10−2 2.14 · 10−4 1.02 · 10−3 8.74 · 10−1 1.83 · 10−2 1.21 · 10−1

168 5.81 · 10−2 2.02 · 10−4 9.71 · 10−4 8.81 · 10−1 1.87 · 10−2 1.31 · 10−1

169 5.52 · 10−2 1.92 · 10−4 9.30 · 10−4 8.86 · 10−1 1.93 · 10−2 1.40 · 10−1

170 5.27 · 10−2 1.84 · 10−4 8.96 · 10−4 8.90 · 10−1 2.02 · 10−2 1.49 · 10−1

171 5.06 · 10−2 1.76 · 10−4 8.66 · 10−4 8.92 · 10−1 2.15 · 10−2 1.57 · 10−1

172 4.87 · 10−2 1.70 · 10−4 8.41 · 10−4 8.95 · 10−1 2.27 · 10−2 1.66 · 10−1

173 4.71 · 10−2 1.64 · 10−4 8.18 · 10−4 8.96 · 10−1 2.43 · 10−2 1.74 · 10−1

174 4.56 · 10−2 1.59 · 10−4 7.98 · 10−4 8.97 · 10−1 2.62 · 10−2 1.83 · 10−1

175 4.43 · 10−2 1.54 · 10−4 7.79 · 10−4 8.97 · 10−1 2.85 · 10−2 1.91 · 10−1

176 4.30 · 10−2 1.50 · 10−4 7.61 · 10−4 8.97 · 10−1 3.14 · 10−2 2.00 · 10−1

177 4.18 · 10−2 1.46 · 10−4 7.44 · 10−4 8.96 · 10−1 3.50 · 10−2 2.08 · 10−1

178 4.07 · 10−2 1.42 · 10−4 7.28 · 10−4 8.93 · 10−1 3.95 · 10−2 2.17 · 10−1

179 3.96 · 10−2 1.38 · 10−4 7.12 · 10−4 8.89 · 10−1 4.59 · 10−2 2.27 · 10−1

180 3.85 · 10−2 1.34 · 10−4 6.95 · 10−4 8.82 · 10−1 5.43 · 10−2 2.37 · 10−1

181 3.73 · 10−2 1.30 · 10−4 6.76 · 10−4 8.74 · 10−1 6.66 · 10−2 2.48 · 10−1

182 3.59 · 10−2 1.25 · 10−4 6.53 · 10−4 8.60 · 10−1 8.27 · 10−2 2.61 · 10−1

183 3.44 · 10−2 1.20 · 10−4 6.27 · 10−4 8.43 · 10−1 1.02 · 10−1 2.77 · 10−1

184 3.30 · 10−2 1.14 · 10−4 6.02 · 10−4 8.26 · 10−1 1.22 · 10−1 2.93 · 10−1

185 3.18 · 10−2 1.10 · 10−4 5.80 · 10−4 8.11 · 10−1 1.39 · 10−1 3.09 · 10−1

186 3.07 · 10−2 1.06 · 10−4 5.61 · 10−4 7.97 · 10−1 1.54 · 10−1 3.25 · 10−1

187 2.97 · 10−2 1.02 · 10−4 5.45 · 10−4 7.85 · 10−1 1.68 · 10−1 3.41 · 10−1

188 2.88 · 10−2 9.93 · 10−5 5.30 · 10−4 7.74 · 10−1 1.78 · 10−1 3.56 · 10−1

189 2.81 · 10−2 9.66 · 10−5 5.17 · 10−4 7.66 · 10−1 1.88 · 10−1 3.70 · 10−1

190 2.75 · 10−2 9.44 · 10−5 5.07 · 10−4 7.60 · 10−1 1.97 · 10−1 3.84 · 10−1

195 2.50 · 10−2 8.50 · 10−5 4.61 · 10−4 7.33 · 10−1 2.25 · 10−1 4.53 · 10−1

200 2.33 · 10−2 7.84 · 10−5 4.28 · 10−4 7.18 · 10−1 2.43 · 10−1 5.21 · 10−1

210 2.10 · 10−2 6.90 · 10−5 3.79 · 10−4 7.05 · 10−1 2.62 · 10−1 6.63 · 10−1

220 1.94 · 10−2 6.21 · 10−5 3.39 · 10−4 6.98 · 10−1 2.73 · 10−1 8.18 · 10−1

November 18, 2011 – 11 : 26 DRAFT 165

Table 54: SM4 Higgs branching fractions for 2-gauge-boson decay channels and total Higgs width in the high-mass region.

MH [GeV] H → gg H → γγ H → Zγ H → WW H → ZZ ΓH [GeV]230 1.81 · 10−2 5.65 · 10−5 3.05 · 10−4 6.95 · 10−1 2.79 · 10−1 9.94 · 10−1

240 1.71 · 10−2 5.20 · 10−5 2.75 · 10−4 6.92 · 10−1 2.84 · 10−1 1.19250 1.62 · 10−2 4.80 · 10−5 2.48 · 10−4 6.93 · 10−1 2.86 · 10−1 1.41260 1.56 · 10−2 4.49 · 10−5 2.26 · 10−4 6.91 · 10−1 2.90 · 10−1 1.65270 1.50 · 10−2 4.22 · 10−5 2.05 · 10−4 6.88 · 10−1 2.93 · 10−1 1.92280 1.46 · 10−2 4.00 · 10−5 1.88 · 10−4 6.88 · 10−1 2.95 · 10−1 2.21290 1.42 · 10−2 3.81 · 10−5 1.72 · 10−4 6.86 · 10−1 2.97 · 10−1 2.53300 1.39 · 10−2 3.65 · 10−5 1.58 · 10−4 6.84 · 10−1 3.00 · 10−1 2.87310 1.38 · 10−2 3.55 · 10−5 1.46 · 10−4 6.80 · 10−1 3.02 · 10−1 3.23320 1.36 · 10−2 3.45 · 10−5 1.35 · 10−4 6.79 · 10−1 3.03 · 10−1 3.63330 1.36 · 10−2 3.39 · 10−5 1.25 · 10−4 6.78 · 10−1 3.03 · 10−1 4.06335 1.37 · 10−2 3.39 · 10−5 1.20 · 10−4 6.77 · 10−1 3.03 · 10−1 4.28336 1.37 · 10−2 3.39 · 10−5 1.20 · 10−4 6.77 · 10−1 3.03 · 10−1 4.32337 1.37 · 10−2 3.39 · 10−5 1.19 · 10−4 6.77 · 10−1 3.02 · 10−1 4.36338 1.38 · 10−2 3.39 · 10−5 1.18 · 10−4 6.76 · 10−1 3.02 · 10−1 4.41339 1.38 · 10−2 3.39 · 10−5 1.17 · 10−4 6.76 · 10−1 3.02 · 10−1 4.45340 1.38 · 10−2 3.40 · 10−5 1.17 · 10−4 6.76 · 10−1 3.02 · 10−1 4.49345 1.39 · 10−2 3.44 · 10−5 1.13 · 10−4 6.69 · 10−1 2.99 · 10−1 4.72346 1.39 · 10−2 3.42 · 10−5 1.11 · 10−4 6.65 · 10−1 2.97 · 10−1 4.79347 1.38 · 10−2 3.38 · 10−5 1.10 · 10−4 6.59 · 10−1 2.94 · 10−1 4.88348 1.37 · 10−2 3.33 · 10−5 1.07 · 10−4 6.51 · 10−1 2.90 · 10−1 5.00349 1.36 · 10−2 3.26 · 10−5 1.05 · 10−4 6.41 · 10−1 2.86 · 10−1 5.14350 1.34 · 10−2 3.19 · 10−5 1.02 · 10−4 6.31 · 10−1 2.81 · 10−1 5.29351 1.32 · 10−2 3.12 · 10−5 9.91 · 10−5 6.21 · 10−1 2.76 · 10−1 5.44352 1.30 · 10−2 3.05 · 10−5 9.66 · 10−5 6.11 · 10−1 2.71 · 10−1 5.60353 1.28 · 10−2 2.98 · 10−5 9.41 · 10−5 6.01 · 10−1 2.66 · 10−1 5.76354 1.26 · 10−2 2.91 · 10−5 9.16 · 10−5 5.92 · 10−1 2.61 · 10−1 5.92355 1.24 · 10−2 2.84 · 10−5 8.91 · 10−5 5.82 · 10−1 2.57 · 10−1 6.09360 1.15 · 10−2 2.53 · 10−5 7.82 · 10−5 5.39 · 10−1 2.38 · 10−1 7.00370 1.01 · 10−2 2.04 · 10−5 6.18 · 10−5 4.73 · 10−1 2.10 · 10−1 8.96375 9.46 · 10−3 1.85 · 10−5 5.56 · 10−5 4.49 · 10−1 1.99 · 10−1 1.00 · 101380 8.94 · 10−3 1.69 · 10−5 5.04 · 10−5 4.28 · 10−1 1.90 · 10−1 1.11 · 101390 8.07 · 10−3 1.44 · 10−5 4.23 · 10−5 3.96 · 10−1 1.77 · 10−1 1.33 · 101400 7.40 · 10−3 1.25 · 10−5 3.63 · 10−5 3.74 · 10−1 1.68 · 10−1 1.55 · 101410 6.85 · 10−3 1.10 · 10−5 3.16 · 10−5 3.59 · 10−1 1.61 · 10−1 1.79 · 101420 6.41 · 10−3 9.85 · 10−6 2.80 · 10−5 3.46 · 10−1 1.56 · 10−1 2.03 · 101430 6.00 · 10−3 8.93 · 10−6 2.51 · 10−5 3.38 · 10−1 1.53 · 10−1 2.27 · 101440 5.68 · 10−3 8.15 · 10−6 2.27 · 10−5 3.31 · 10−1 1.51 · 10−1 2.52 · 101450 5.37 · 10−3 7.51 · 10−6 2.06 · 10−5 3.27 · 10−1 1.50 · 10−1 2.76 · 101460 5.10 · 10−3 6.97 · 10−6 1.89 · 10−5 3.24 · 10−1 1.49 · 10−1 3.02 · 101470 4.87 · 10−3 6.51 · 10−6 1.75 · 10−5 3.22 · 10−1 1.49 · 10−1 3.27 · 101480 4.65 · 10−3 6.11 · 10−6 1.62 · 10−5 3.21 · 10−1 1.50 · 10−1 3.53 · 101490 4.47 · 10−3 5.76 · 10−6 1.51 · 10−5 3.21 · 10−1 1.51 · 10−1 3.80 · 101500 4.28 · 10−3 5.46 · 10−6 1.41 · 10−5 3.22 · 10−1 1.51 · 10−1 4.06 · 101550 3.55 · 10−3 4.38 · 10−6 1.05 · 10−5 3.31 · 10−1 1.59 · 10−1 5.46 · 101600 2.99 · 10−3 3.74 · 10−6 8.21 · 10−6 3.46 · 10−1 1.69 · 10−1 6.99 · 101650 2.55 · 10−3 3.33 · 10−6 6.62 · 10−6 3.65 · 10−1 1.80 · 10−1 8.68 · 101700 2.17 · 10−3 3.07 · 10−6 5.46 · 10−6 3.86 · 10−1 1.91 · 10−1 1.06 · 102750 1.86 · 10−3 2.89 · 10−6 4.57 · 10−6 4.06 · 10−1 2.03 · 10−1 1.27 · 102800 1.60 · 10−3 2.78 · 10−6 3.88 · 10−6 4.27 · 10−1 2.15 · 10−1 1.52 · 1021000 8.08 · 10−4 2.85 · 10−6 2.28 · 10−6 5.02 · 10−1 2.54 · 10−1 2.88 · 102

November 18, 2011 – 11 : 26 DRAFT 166

Table 55: SM4 Higgs branching fractions for 4-fermion final states in the low- and intermediate-mass region withl = e, µ, τ, νe, νµ, ντ andq = u, d, c, s, b.

MH [GeV] H → 4e H → 2e2µ H → 4l H → 4q H → 2l2q H → 4f100 2.26 · 10−7 3.31 · 10−7 1.67 · 10−4 7.48 · 10−4 7.85 · 10−4 1.70 · 10−3

110 7.81 · 10−7 1.27 · 10−6 7.32 · 10−4 3.53 · 10−3 3.36 · 10−3 7.62 · 10−3

120 2.76 · 10−6 4.99 · 10−6 2.36 · 10−3 1.17 · 10−2 1.08 · 10−2 2.48 · 10−2

130 8.00 · 10−6 1.48 · 10−5 6.12 · 10−3 3.05 · 10−2 2.78 · 10−2 6.44 · 10−2

140 1.83 · 10−5 3.51 · 10−5 1.38 · 10−2 6.88 · 10−2 6.24 · 10−2 1.45 · 10−1

145 2.54 · 10−5 4.89 · 10−5 1.99 · 10−2 9.98 · 10−2 8.99 · 10−2 2.10 · 10−1

150 3.33 · 10−5 6.42 · 10−5 2.91 · 10−2 1.45 · 10−1 1.31 · 10−1 3.05 · 10−1

151 3.48 · 10−5 6.71 · 10−5 3.14 · 10−2 1.56 · 10−1 1.41 · 10−1 3.29 · 10−1

152 3.61 · 10−5 6.96 · 10−5 3.39 · 10−2 1.68 · 10−1 1.52 · 10−1 3.54 · 10−1

153 3.71 · 10−5 7.11 · 10−5 3.66 · 10−2 1.82 · 10−1 1.64 · 10−1 3.82 · 10−1

154 3.79 · 10−5 7.34 · 10−5 3.97 · 10−2 1.97 · 10−1 1.77 · 10−1 4.14 · 10−1

155 3.84 · 10−5 7.45 · 10−5 4.31 · 10−2 2.14 · 10−1 1.92 · 10−1 4.49 · 10−1

156 3.85 · 10−5 7.42 · 10−5 4.66 · 10−2 2.30 · 10−1 2.10 · 10−1 4.86 · 10−1

157 3.80 · 10−5 7.33 · 10−5 5.08 · 10−2 2.51 · 10−1 2.27 · 10−1 5.29 · 10−1

158 3.61 · 10−5 6.98 · 10−5 5.62 · 10−2 2.76 · 10−1 2.50 · 10−1 5.82 · 10−1

159 3.34 · 10−5 6.47 · 10−5 6.18 · 10−2 3.02 · 10−1 2.75 · 10−1 6.39 · 10−1

160 2.95 · 10−5 5.75 · 10−5 6.85 · 10−2 3.31 · 10−1 3.05 · 10−1 7.04 · 10−1

161 2.54 · 10−5 4.96 · 10−5 7.45 · 10−2 3.60 · 10−1 3.30 · 10−1 7.64 · 10−1

162 2.23 · 10−5 4.32 · 10−5 7.90 · 10−2 3.81 · 10−1 3.49 · 10−1 8.09 · 10−1

163 2.05 · 10−5 3.97 · 10−5 8.19 · 10−2 3.96 · 10−1 3.61 · 10−1 8.38 · 10−1

164 1.95 · 10−5 3.78 · 10−5 8.36 · 10−2 4.04 · 10−1 3.70 · 10−1 8.58 · 10−1

165 1.91 · 10−5 3.70 · 10−5 8.50 · 10−2 4.11 · 10−1 3.76 · 10−1 8.73 · 10−1

166 1.91 · 10−5 3.69 · 10−5 8.59 · 10−2 4.16 · 10−1 3.81 · 10−1 8.83 · 10−1

167 1.93 · 10−5 3.76 · 10−5 8.66 · 10−2 4.20 · 10−1 3.84 · 10−1 8.91 · 10−1

168 1.98 · 10−5 3.85 · 10−5 8.72 · 10−2 4.23 · 10−1 3.87 · 10−1 8.98 · 10−1

169 2.04 · 10−5 3.99 · 10−5 8.77 · 10−2 4.26 · 10−1 3.90 · 10−1 9.03 · 10−1

170 2.13 · 10−5 4.17 · 10−5 8.81 · 10−2 4.29 · 10−1 3.92 · 10−1 9.08 · 10−1

171 2.24 · 10−5 4.35 · 10−5 8.84 · 10−2 4.31 · 10−1 3.93 · 10−1 9.12 · 10−1

172 2.38 · 10−5 4.62 · 10−5 8.87 · 10−2 4.32 · 10−1 3.95 · 10−1 9.16 · 10−1

173 2.54 · 10−5 5.01 · 10−5 8.90 · 10−2 4.34 · 10−1 3.96 · 10−1 9.19 · 10−1

174 2.74 · 10−5 5.40 · 10−5 8.92 · 10−2 4.35 · 10−1 3.97 · 10−1 9.22 · 10−1

175 2.97 · 10−5 5.88 · 10−5 8.94 · 10−2 4.37 · 10−1 3.98 · 10−1 9.24 · 10−1

176 3.28 · 10−5 6.48 · 10−5 8.96 · 10−2 4.38 · 10−1 3.99 · 10−1 9.27 · 10−1

177 3.65 · 10−5 7.21 · 10−5 8.97 · 10−2 4.39 · 10−1 4.00 · 10−1 9.29 · 10−1

178 4.14 · 10−5 8.12 · 10−5 8.98 · 10−2 4.41 · 10−1 4.01 · 10−1 9.31 · 10−1

179 4.75 · 10−5 9.42 · 10−5 8.99 · 10−2 4.42 · 10−1 4.01 · 10−1 9.33 · 10−1

180 5.64 · 10−5 1.11 · 10−4 8.98 · 10−2 4.44 · 10−1 4.02 · 10−1 9.36 · 10−1

181 6.85 · 10−5 1.36 · 10−4 9.00 · 10−2 4.44 · 10−1 4.03 · 10−1 9.38 · 10−1

182 8.57 · 10−5 1.69 · 10−4 9.01 · 10−2 4.46 · 10−1 4.04 · 10−1 9.40 · 10−1

183 1.06 · 10−4 2.09 · 10−4 9.02 · 10−2 4.48 · 10−1 4.05 · 10−1 9.43 · 10−1

184 1.26 · 10−4 2.49 · 10−4 9.02 · 10−2 4.49 · 10−1 4.06 · 10−1 9.46 · 10−1

185 1.44 · 10−4 2.86 · 10−4 9.03 · 10−2 4.51 · 10−1 4.07 · 10−1 9.48 · 10−1

186 1.59 · 10−4 3.18 · 10−4 9.05 · 10−2 4.52 · 10−1 4.07 · 10−1 9.50 · 10−1

187 1.73 · 10−4 3.44 · 10−4 9.07 · 10−2 4.54 · 10−1 4.07 · 10−1 9.52 · 10−1

188 1.84 · 10−4 3.67 · 10−4 9.02 · 10−2 4.56 · 10−1 4.07 · 10−1 9.53 · 10−1

189 1.94 · 10−4 3.87 · 10−4 9.03 · 10−2 4.57 · 10−1 4.07 · 10−1 9.55 · 10−1

190 2.03 · 10−4 4.04 · 10−4 9.04 · 10−2 4.57 · 10−1 4.09 · 10−1 9.56 · 10−1

195 2.31 · 10−4 4.63 · 10−4 9.07 · 10−2 4.61 · 10−1 4.09 · 10−1 9.60 · 10−1

200 2.49 · 10−4 4.99 · 10−4 9.06 · 10−2 4.63 · 10−1 4.10 · 10−1 9.64 · 10−1

210 2.68 · 10−4 5.38 · 10−4 9.05 · 10−2 4.66 · 10−1 4.11 · 10−1 9.68 · 10−1

220 2.78 · 10−4 5.59 · 10−4 9.06 · 10−2 4.68 · 10−1 4.13 · 10−1 9.72 · 10−1

November 18, 2011 – 11 : 26 DRAFT 167

Table 56: SM4 Higgs branching fractions for 4-fermion final states in the high-mass region withl =

e, µ, τ, νe, νµ, ντ andq = u, d, c, s, b.

MH [GeV] H → 4e H → 2e2µ H → 4l H → 4q H → 2l2q H → 4f230 2.83 · 10−4 5.70 · 10−4 9.04 · 10−2 4.70 · 10−1 4.14 · 10−1 9.74 · 10−1

240 2.88 · 10−4 5.80 · 10−4 9.04 · 10−2 4.71 · 10−1 4.15 · 10−1 9.76 · 10−1

250 2.90 · 10−4 5.86 · 10−4 9.05 · 10−2 4.71 · 10−1 4.16 · 10−1 9.78 · 10−1

260 2.93 · 10−4 5.92 · 10−4 9.05 · 10−2 4.72 · 10−1 4.16 · 10−1 9.79 · 10−1

270 2.95 · 10−4 5.97 · 10−4 9.05 · 10−2 4.73 · 10−1 4.17 · 10−1 9.80 · 10−1

280 2.98 · 10−4 6.02 · 10−4 9.06 · 10−2 4.73 · 10−1 4.17 · 10−1 9.81 · 10−1

290 2.99 · 10−4 6.08 · 10−4 9.06 · 10−2 4.74 · 10−1 4.18 · 10−1 9.82 · 10−1

300 3.00 · 10−4 6.10 · 10−4 9.05 · 10−2 4.74 · 10−1 4.18 · 10−1 9.82 · 10−1

310 3.03 · 10−4 6.14 · 10−4 9.07 · 10−2 4.75 · 10−1 4.17 · 10−1 9.82 · 10−1

320 3.03 · 10−4 6.14 · 10−4 9.06 · 10−2 4.75 · 10−1 4.16 · 10−1 9.82 · 10−1

330 3.03 · 10−4 6.14 · 10−4 9.04 · 10−2 4.75 · 10−1 4.16 · 10−1 9.81 · 10−1

335 3.03 · 10−4 6.13 · 10−4 9.02 · 10−2 4.74 · 10−1 4.15 · 10−1 9.80 · 10−1

336 3.02 · 10−4 6.13 · 10−4 9.02 · 10−2 4.74 · 10−1 4.15 · 10−1 9.80 · 10−1

337 3.02 · 10−4 6.13 · 10−4 9.02 · 10−2 4.74 · 10−1 4.15 · 10−1 9.79 · 10−1

338 3.02 · 10−4 6.12 · 10−4 9.01 · 10−2 4.74 · 10−1 4.15 · 10−1 9.79 · 10−1

339 3.02 · 10−4 6.11 · 10−4 9.00 · 10−2 4.74 · 10−1 4.15 · 10−1 9.79 · 10−1

340 3.02 · 10−4 6.11 · 10−4 8.99 · 10−2 4.74 · 10−1 4.14 · 10−1 9.78 · 10−1

345 2.98 · 10−4 6.02 · 10−4 8.88 · 10−2 4.69 · 10−1 4.10 · 10−1 9.68 · 10−1

346 2.96 · 10−4 5.98 · 10−4 8.83 · 10−2 4.66 · 10−1 4.07 · 10−1 9.62 · 10−1

347 2.93 · 10−4 5.92 · 10−4 8.75 · 10−2 4.62 · 10−1 4.04 · 10−1 9.53 · 10−1

348 2.90 · 10−4 5.85 · 10−4 8.65 · 10−2 4.57 · 10−1 3.99 · 10−1 9.42 · 10−1

349 2.86 · 10−4 5.76 · 10−4 8.52 · 10−2 4.50 · 10−1 3.93 · 10−1 9.28 · 10−1

350 2.81 · 10−4 5.67 · 10−4 8.38 · 10−2 4.42 · 10−1 3.86 · 10−1 9.12 · 10−1

351 2.76 · 10−4 5.53 · 10−4 8.24 · 10−2 4.35 · 10−1 3.80 · 10−1 8.97 · 10−1

352 2.72 · 10−4 5.45 · 10−4 8.11 · 10−2 4.27 · 10−1 3.74 · 10−1 8.82 · 10−1

353 2.68 · 10−4 5.37 · 10−4 7.98 · 10−2 4.21 · 10−1 3.67 · 10−1 8.68 · 10−1

354 2.64 · 10−4 5.28 · 10−4 7.83 · 10−2 4.14 · 10−1 3.61 · 10−1 8.54 · 10−1

355 2.60 · 10−4 5.20 · 10−4 7.71 · 10−2 4.07 · 10−1 3.56 · 10−1 8.40 · 10−1

360 2.41 · 10−4 4.82 · 10−4 7.15 · 10−2 3.77 · 10−1 3.30 · 10−1 7.78 · 10−1

370 2.13 · 10−4 4.25 · 10−4 6.30 · 10−2 3.31 · 10−1 2.90 · 10−1 6.83 · 10−1

375 2.02 · 10−4 4.04 · 10−4 5.98 · 10−2 3.13 · 10−1 2.75 · 10−1 6.48 · 10−1

380 1.93 · 10−4 3.87 · 10−4 5.72 · 10−2 2.99 · 10−1 2.62 · 10−1 6.19 · 10−1

390 1.80 · 10−4 3.60 · 10−4 5.31 · 10−2 2.77 · 10−1 2.43 · 10−1 5.73 · 10−1

400 1.71 · 10−4 3.42 · 10−4 5.02 · 10−2 2.61 · 10−1 2.30 · 10−1 5.41 · 10−1

410 1.64 · 10−4 3.29 · 10−4 4.82 · 10−2 2.50 · 10−1 2.21 · 10−1 5.19 · 10−1

420 1.60 · 10−4 3.19 · 10−4 4.67 · 10−2 2.42 · 10−1 2.14 · 10−1 5.03 · 10−1

430 1.57 · 10−4 3.14 · 10−4 4.57 · 10−2 2.36 · 10−1 2.09 · 10−1 4.91 · 10−1

440 1.55 · 10−4 3.10 · 10−4 4.49 · 10−2 2.32 · 10−1 2.05 · 10−1 4.82 · 10−1

450 1.54 · 10−4 3.07 · 10−4 4.44 · 10−2 2.30 · 10−1 2.03 · 10−1 4.77 · 10−1

460 1.54 · 10−4 3.06 · 10−4 4.41 · 10−2 2.28 · 10−1 2.01 · 10−1 4.73 · 10−1

470 1.54 · 10−4 3.07 · 10−4 4.39 · 10−2 2.27 · 10−1 2.00 · 10−1 4.71 · 10−1

480 1.54 · 10−4 3.09 · 10−4 4.39 · 10−2 2.27 · 10−1 2.00 · 10−1 4.71 · 10−1

490 1.55 · 10−4 3.11 · 10−4 4.40 · 10−2 2.27 · 10−1 2.01 · 10−1 4.71 · 10−1

500 1.56 · 10−4 3.13 · 10−4 4.41 · 10−2 2.27 · 10−1 2.01 · 10−1 4.73 · 10−1

550 1.63 · 10−4 3.29 · 10−4 4.57 · 10−2 2.35 · 10−1 2.08 · 10−1 4.89 · 10−1

600 1.74 · 10−4 3.51 · 10−4 4.81 · 10−2 2.48 · 10−1 2.19 · 10−1 5.15 · 10−1

650 1.86 · 10−4 3.74 · 10−4 5.10 · 10−2 2.62 · 10−1 2.32 · 10−1 5.45 · 10−1

700 1.99 · 10−4 4.00 · 10−4 5.41 · 10−2 2.77 · 10−1 2.46 · 10−1 5.77 · 10−1

750 2.12 · 10−4 4.26 · 10−4 5.73 · 10−2 2.92 · 10−1 2.60 · 10−1 6.10 · 10−1

800 2.24 · 10−4 4.52 · 10−4 6.05 · 10−2 3.08 · 10−1 2.74 · 10−1 6.42 · 10−1

1000 2.70 · 10−4 5.42 · 10−4 7.21 · 10−2 3.60 · 10−1 3.23 · 10−1 7.56 · 10−1

November 18, 2011 – 11 : 26 DRAFT 168

γγ(×100)bbggZZ

WW

MH [GeV]

BR(SM4)/BR(SM)

600500400300200100

100

10

1

0.1

Fig. 84: Ratio of branching fractions in SM4 with respect to SM3 forWW, ZZ, gg, andbb decay channels.

Table 57: NLO EW corrections to the decayH → γγ according to Eq.(102).

MH [GeV] δ [%] missing H.O.[%]

90 −53.9 ±13.995 −59.2 ±13.9100 −64.5 ±13.9105 −69.5 ±13.9110 −74.4 ±13.9115 −79.0 ±13.9120 −83.3 ±13.9125 −87.3 +13.9−12.7130 −90.8 +13.9−9.2135 −94.0 +13.9−6.0140 −96.6 +13.9−3.4145 −98.5 +13.9−1.5150 −99.7 +13.9−0.3

Table 58: Higgs branching fractions forγγ decay channel with and without NLO EW corrections.

MH [GeV] w/o NLO EW w/ NLO EW

100 1.31 · 10−4 4.65 · 10−5

110 1.72 · 10−4 4.40 · 10−5

120 2.26 · 10−4 3.77 · 10−5

130 2.95 · 10−4 2.71 · 10−5

140 3.81 · 10−4 1.30 · 10−5

150 4.74 · 10−4 1.42 · 10−6

November 18, 2011 – 11 : 26 DRAFT 169

15 The (heavy) Higgs boson lineshape3338

413339


In this Section we consider the problem of a consistent definition of the Higgs–boson-lineshape at LHC3341

and address the question of optimal presentation of LHC data.3342

Some preliminary observations are needed: the Higgs systemof the Standard Model has almost a3343

non-perturbative behavior, even at a low scale. Let us consider the traditional on-shell approach and the3344

values for the on-shell decay width of the Higgs boson.3345

ForMH = 140 GeV the total width is8.12 × 10−3 GeV. The processH → bb has a partial with3346

of 2.55 × 10−3 GeV, other two-body decays are almost negligible whileH → 4 f has4.64× 10−3 GeV3347

well below theWW -threshold. Therefore the four-body decay, even below threshold, is more important3348

than the two-body ones. What are the corresponding implications? Since decay widths are related to3349

the imaginary parts of loop diagrams the above statement is equivalent to say that, in terms of imaginary3350

parts of theH self-energy, three-loop diagrams are as important as one-loop diagrams.3351

We realize that most of the people just want to use some well-defined recipe without having to3352

dig any deeper; however, there is no alternative to a complete description of LHC processes which has3353

to include the complete matrix elements for all processes; splitting the wholeS -matrix element into3354

components is just conventional wisdom. However, the precise tone and degree of formality must be3355

dictated by gauge invariance.3356

The framework discussed in this Section is general enough and can be used for all processes and3357

for all kinematical regions; however, here the main focus will be on the description of the Higgs–boson-3358

lineshape in the heavy Higgs region, typically above600 GeV. The general argument is well documented3359

in the literature and, for a complete description of all technical details, we refer to Ref. [149, 324]. Part3360

of the results discussed in this Section and concerning a correct implementation of the Higgs–boson-3361

lineshape have been summarized in a talk at the BNL meeting ofthe HXSWG.423362

One might wonder why considering a SM Higgs boson in such a high-mass range. There are3363

are classic constraints on the Higgs boson mass coming from unitarity, triviality and vacuum stability,3364

precision electroweak data and absence of fine-tuning. However, the search for a SM Higgs boson over3365

a mass range from80 GeV to 1 TeV is clearly indicated as a priority in many experimental papers,3366

e.g.,ATLAS: letter of intent for a general-purpose pp experimentat the large hadron collider at CERN43.3367

Coming back to the framework that we are introducing here, there is another important issue: when3368

working in the on-shell scheme one finds tht the two-loop corrections to the on-shell Higgs width exceed3369

the one-loop corrections if the on-shell Higgs mass is larger than900 GeV, as discussed in Ref. [325].3370

This fact simply tells you that peturbation theory divergesbadly, starting from approximately1 TeV.3371

Recently the problem of going beyond the zero-width approximation has received new boost from3372

the work of Ref. [326]: the programIHIXS allow the study of the Higgs–boson-lineshape for a finite3373

width of the Higgs boson and computes the cross-section sampling over a Breit-Wigner distribution.3374

To start our discussion we consider the processij → H(→ f)+X wherei, j ∈ partons andf is a3375

generic final state (e.g.,f = γγ, 4 f , etc.). For the sake of simplicity we neglect, for a moment, folding the3376

partonic process with parton distribution functions (PDFs). Since the Higgs boson is a scalar resonance3377

we can split the whole process into three parts,production, propagationanddecay.3378

41G. Passarino convener, S. Goria, D. Rosco42http://www.bnl.gov/hcs/43http://atlas.web.cern.ch/Atlas/internal/tdr.html

November 18, 2011 – 11 : 26 DRAFT 170

15.2 Propagation3379

In Quantum Field Theory (QFT) amplitudes are made out of propagators and vertices: the Higgs (Dyson-3380

resummed) propagator reads as follows:3381

∆H(s) =[s−M2

H + SHH

(s,Mt,MH,MW,MZ

)]−1, (104)

whereMi is a renormalized mass andSHH is the renormalized Higgs self-energy (to all orders but3382

with one-particle-irreducible diagrams). The first argument of the self-energy is the external momen-3383

tum squared, the remaining ones are (renormalized) masses in the loops. We define complex poles for3384

unstable particles as the (complex) solutions of the following system:3385

sH −M2H + SHH

(sH,Mt,MH,MW,MZ

)= 0,

sW −M2W + SWW

(sW,Mt,MH,MW,MZ

)= 0, (105)

etc. To lowest order accuracy the Higgs propagator is rewritten as3386

∆−1H = s− sH. (106)

The complex pole describing an unstable particle is conventionally parametrized as3387

si = µ2i − i µi γi, (107)

whereµi is an input parameter (similar to the on-shell mass) whileγi can be computed (as the on-shell3388

total width), say within the Standard Model (SM). Note that the the pole of∆ fully embodies the prop-3389

agation properties of a particle. We know that even in ordinary Quantum Mechanics the resonances are3390

described as the complex energy poles in the scattering amplitude. The general formalism for describing3391

unstable particles in QFT was developed long ago, see Ref. [327–331]; for an implementation in gauge3392

theories we refer to the work of Ref. [332–335].3393

Consider the complex mass scheme (CMS) introduced in Ref. [336] and extended at two-loop3394

level in Ref. [337]: here, at lowest level of accuracy, we use3395

sH −M2H + SHH

(sH, st, sH, sW, sZ

)= 0, (108)

where nowSHH is computed at one loop level andsW etc. are the experimental complex poles, derived3396

from the corresponding on-shell masses and widths. For theW andZ bosons the input parameter set3397

(IPS) is defined in terms of pseudo-observables; at first, on-shell quantities are derived by fitting the3398

experimental lineshapes with3399

ΣVV(s) =N

(s−M2OS)

2 + s2 Γ2OS/M

2OS

, V = W,Z, (109)

whereN is an irrelevant (for our purposes) normalization constant. Secondly, we define pseudo-observables3400

MP =MOS cosψ, ΓP = ΓOS sinψ, ψ = arctanΓOS

MOS, (110)

which are inserted in the IPS.3401

Renormalization with complex poles should not be confused with a simple recipe for the replace-3402

ment of running widths with constant widths; there are many more ingredients in the scheme. It is worth3403

noting that perturbation theory based onsH instead of the on-shell mass has much better convergence3404

properties; indeed, as shown in Ref. [325], the two-loop corrections to the imaginary part ofsH become3405

as large as the one-loop onesonly whenµH = 1.74 TeV. This suggests that the complex pole scheme is3406

preferable also from the point of view of describing the heavy H-boson production at LHC.3407

November 18, 2011 – 11 : 26 DRAFT 171

There is a substantial difference betweenW,Z complex poles and the Higgs complex pole. In3408

the first caseW,Z bosons decay predominantly into two (massless) fermions while for the Higgs boson3409

below theWW -threshold the decay into four fermions is even larger than the decay into abb pair.3410

Therefore we cannot use for the Higgs boson the well-known result, valid forW,Z,3411

ImSVV(s) ≈ΓOSV

MOSV

s. (111)

As a consequence of this fact we have3412

γV = ΓOSV

[1− 1

2

( ΓOSV

MOSV

)2]+HO, (112)

where the perturbative expansion is well under control sinceΓOSV /MOS

V << 1. For the Higgs boson we3413

have a different expansion,3414

γH = ΓH

[1 +

∑

n

an ΓnH

]+

∑

V=W,Z

ΓVMV

MH

∑

n,l

bVnl ΓnV Γl

H,

a1 = −[Im Sh

HH ,OS

]2,

a2 =1

2

[ 1

MHIm Sh

HH ,OS − MH Im ShhHH ,OS

],

bV10 = − Re SvHH ,OS +Re Sv

HH ,OS Re ShHH ,OS − Im Sv

HH ,OS Im ShHH ,OS

bV11 =1

2MHIm Sv

HH ,OS −MH Im ShvHH ,OS,

bV20 = −1

2

MV

MHIm Svv

HH ,OS (113)

Here we haveMi =MOSi , Γi = ΓOS

i (on-shell quantities) and3415

SaHH ,OS =

∂

∂M2a

SHH

(M2

H,Mt,MH,MW,MZ

),

SabHH ,OS =

∂2

∂M2a∂M

2b

SHH

(M2

H,Mt,MH,MW,MZ

), (114)

where only the first few terms in the perturbative expansion are given. In Eq.(113) we used the following3416

definition of the on-shell width3417

ΓOSH MOS

H = Im SHH ,OS +HO (115)

Only the complex pole is gauge-parameter independent to allorders of perturbation theory while on-3418

shell quantities are ill-defined beyond lowest order. Indeed, in theRξ gauge, at lowest order, one has the3419

following expression for the bosonic part:3420

Im SHH , bos=g2

4M2W

s2[(

1−M4

H

s2

) (1− 4 ξW

M2W

s

)1/2

θ(s− 4 ξWM

2W

)+

1

2(W → Z)

],

(116)whereξV (V = W,Z) are gauge parameters. Note that Eq.(113) (the expansion) involves derivatives.3421

A technical remark: suppose that we useµH as afree input parameter and deriveγH in the SM3422

from the equation3423

µH γH = Im SHH

(sH, st, sH, sW, sZ

). (117)

November 18, 2011 – 11 : 26 DRAFT 172

Table 59: The Higgs boson complex pole at fixed values of theW, t complex poles compared with the completesolution forsH, sW andst

µH [ GeV] γW [ GeV] fixed γt [ GeV] fixed γH [ GeV] derived200 2.093 1.481 1.264250 3.369300 7.721

µH [ GeV] γW [ GeV] derived γt [ GeV] derived γH [ GeV] derived200 1.932 1.171 1.262250 1.822 0.923 3.364300 1.738 0.689 7.711

Since the bareW,Z masses are replaced with complex poles also in couplings (topreserve gauge invari-3424

ance) it follows thatγH (solution of Eq.(117)) is renormalization scale dependent; while counterterms3425

can be introduced to make the self-energy ultraviolet finite, theµR dependence drops only in subtracted3426

quantities, i.e., after final renormalization, something that would require knowledge of the experimental3427

Higgs complex pole. Following our intuition we fix the scale at µH.3428

After evaluating the coefficients of Eq.(113) (e.g., in theξ = 1 gauge) it is easily seen that the3429

expanded solution of Eq.(108) is not a good approximation toexact one, especially for high values of3430

µH. For instance, forµH = 500 GeV we have an exact solutionγH = 58.85 GeV, an expanded one of3431

62.87 GeV with an on-shell with of68.0 GeV. Therefore, we will use an exact, numerical, solution for3432

γH; details on the structure of the Higgs self-energy to all orders of perturbation theory can be found in3433

Ref. [337,338].3434

To computeγH at the same level of accuracy to whichΓOSH is known (see Ref. [6]) would require,3435

at least, a three-loop calculation (the first instance wherewe have a four-fermion cut of the Higgs self-3436

energy).3437

Complex poles for unstableW,Z,H andt also tell us that it is very difficult for an heavy Higgs3438

boson to come out right within the SM; these complex poles aresolutions of a (coupled) system of3439

equations but forW,Z and (partially)t we can compare with the corresponding experimental quantities.3440

Results are shown in Table 59 and clearly indicate mismatches between predicted and experimentalW, t3441

complex poles. Indeed, as soon asµH increases, it becomes more and more difficult to find complex3442

W, t andZ poles with an imaginary part compatible with measurements.3443

This simple fact raises the following question: what is the physical meaning of an heavy Higgs3444

boson search? We have the usual and well-known considerations: a Higgs boson above600 GeV requires3445

new physics at1 TeV, argument based an partial-wave unitarity (which should not be taken quantitatively3446

or too literally); violation of unitarity bound possibly implies the presence ofJ = 0, 1 resonances but3447

there is no way to predict their masses, simply scaling theπ−π system gives resonances in the1 TeV3448

ballpark. Generally speaking, it would be a good idea to address this search assearchfor J = 0, 1 heavy3449

resonances decaying intoVV → 4 f .3450

In a model independent approach bothµH andγH should be kept free in order to perform a2dim3451

scan of the Higgs-boson lineshape. For the high-mass regionthis remains the recommended strategy.3452

Once the fits are performed it will be left to theorists to struggle with the SM interpretation of the results.3453

November 18, 2011 – 11 : 26 DRAFT 173

To summarize, we have addressed the following question: what is the common sense definition of3454

mass and width of the Higgs boson? We have several options,3455

sH = µ2H − i µH γH, sH =

(µ′H − i

2γ′H

)2

, sH =M

2H − iΓHMH

1 + Γ2H/M

2H

. (118)

We may ask which one is correct, approximate or closer to the experimental peak. Here we have to3456

distinguish: forγH ≪ µH MH is a good approximation to the on-shell mass and it is closer to the3457

experimental peak; for instance, for theZ bosonMZ is equivalent to the mass measured at Lep. However,3458

in the high-mass scenario, whereγH ∼ µH, the situation changes anOH 6= OOSH for any observable (or3459

pseudo-observable). Therefore, the message is: do not use the computed on-shell width to estimateMH.3460

15.3 Production and decay3461

Before describing production and decay of an Higgs boson we underline the general structure of any3462

process containing a Higgs boson intermediate state. The corresponding amplitude is given by3463

A(s) =f(s)

s− sH+N(s), (119)

whereN(s) denotes the part of the amplitude which is non-resonant. Signal and background are defined3464

as3465

A(s) = S(s) +B(s), S(s) =f(sH)

s− sH, B(s) =

f(s)− f(sH)

s− sH+N(s). (120)

As a first step we will show how to writef(s) in a way such that pseudo-observables make their appear-3466

ance. Consider the processij → H → f wherei, j ∈ partons; the complete cross-section will be written3467

as follows:3468

σ (ij → H → f) =1

s

∫dΦij→f

[∑

s,c

∣∣∣A (ij → H)∣∣∣2] 1∣∣∣s− sH

∣∣∣2

[∑

s,c

∣∣∣A (H → f)∣∣∣2], (121)

where∑

spin,col is over spin and colors (averaging on the initial state). Note that the background (e.g.,3469

gg → 4 f ) has not been included and, strictly speaking and for reasons of gauge invariance, one should3470

consider only the residue of the Higgs-resonant amplitude at the complex pole, as described in Eq.(120).3471

For the moment we will argue that the dominant corrections are the QCD ones where we have no problem3472

of gauge parameter dependence. If we decide to keep the Higgsboson off-shell also in the resonant part3473

of the amplitude (interference S/B remains unaddressed) then we can write3474

∑

s,c

∣∣∣A (ij → H)∣∣∣2= s Fij(s). (122)

For instance, we have3475

Fgg(s) =α2s

π2GF s

288√2

∣∣∣∑

q

f (τq)∣∣∣2(1 + δQCD) , (123)

whereτq = 4m2q/s, f(τq) is defined in Eq.(3) of Ref. [63] and whereδQCD gives the QCD corrections3476

to gg → H up to NNLO + NLL order. Furthermore, we define3477

ΓH→f =1√s

∫dΦH→f

∑

s,c

∣∣∣A (H → f)∣∣∣2, (124)

November 18, 2011 – 11 : 26 DRAFT 174

which gives the partial decay width of a Higgs boson of virtuality s into a final statef .3478

σij→H =Fij(s)

s, (125)

which gives the production cross-section of a Higgs boson ofvirtuality s. We can write the final result in3479

terms of pseudo-observables3480

σ (ij → H → f) = σij→Hs2∣∣∣s− sH

∣∣∣2

ΓH→f√s. (126)

It is also convenient to rewrite the result as3481

σ (ij → H → f) = σij→Hs2∣∣∣s− sH

∣∣∣2

ΓtotH√s

BR(H → f) , (127)

where we have introduced a sum over all final states,3482

ΓtotH =

∑

f

Γ (H → f) . (128)

Note that we have written the phase-space integral fori(p1) + j(p2) → f as3483

∫dΦij→f =

∫ ∏

f

d4pf δ+(p2f ) δ

4(p1 + p2 −∑

f

pf )

=

∫d4k δ4(k − p1 − p2)

∫ ∏

f

d4pf δ+(p2f ) δ

4(k −∑

f

pf ), (129)

where we assume that all initial and final states (e.g.,γγ, 4 f , etc.) are massless. It is worth nothing that3484

the introduction of complex poles does not imply complex kinematics. According to Eq.(120) only the3485

residue of the propagator at the complex pole becomes complex, not any element of the phase-space3486

integral.3487

– DefinitionWe define an off-shell production cross-section (for all channels) as follows:3488

σpropij→all = σij→H

s2∣∣∣s− sH

∣∣∣2

ΓtotH√s. (130)

When the cross-sectionij → H refers to an off-shell Higgs boson the choice of the QCD scales should3489

be made according to the virtuality and not to a fixed value. Therefore, always referring to Figure 91,3490

for the PDFs andσij→H+X one should selectµ2F= µ2R = v s/2 (v s being the invariant mass of the3491

incoming partons).3492

The off-shell Higgs production is currently computed according to the replacement3493

σOS(µ2H) δ(z s− µ2H) =⇒ σOFS(z s)BW(z s), (131)

(e.g., see Ref. [104]) at least at lowest QCD order, where theso-called modified Breit–Wigner distribution3494

is defined by3495

BW(s) =1

π

sΓOSH /µH

(s− µ2H

)2+(sΓOS

H /µH

)2 , (132)

November 18, 2011 – 11 : 26 DRAFT 175

Table 60: Higgs boson complex pole;ΓOSH is the on-shell width,γH is defined in Eq.(107) and the Bar-scheme in

Eq.(134).

µH[ GeV] ΓOSH [ GeV] (YR) γH [ GeV] MH[ GeV] ΓH[ GeV]

200 1.43 1.26 200 1.26400 29.2 24.28 400.7 24.24600 123 102.17 608.6 100.72700 199 159.54 717.95 155.55800 304 228.44 831.98 219.66900 449 307.63 951.12 291.09

where nowµH = MOSH . This ad-hoc Breit–Wigner cannot be derived from QFT and also is not nor-3496

malizable in[0 , +∞]. Note that this Breit–Wigner for a running width comes from the substitution of3497

Γ → Γ(s) = Γ s/M2 in the Breit–Wigner for a fixed widthΓ. This substitution is not justifiable. Its3498

practical purpose is to enforce aphysicalbehavior for low virtualities of the Higgs boson but the usage3499

cannot be justified or recommended. For instance, if one considersVV scattering and uses this distri-3500

bution in thes -channel Higgs exchange, the behavior for large values ofs spoils unitarity cancellation3501

with the contact diagram. It is worth noting that the alternative replacement3502

σOS(µ2H) δ(z s− µ2H) =⇒ σOFS(z s)BW(z s), BW(z s) =

1

π

MH ΓOSH(

z s− µ2H

)2+(µH ΓOS

H

)2 , (133)

has additional problems at the low energy tail of the resonance due to thegg -luminosity, creating an3503

artificial increase of the lineshape at low virtualities.3504

Another important issue is thatγH which appears in the imaginary part of the inverse Dyson-3505

resummed propagator is not the on-shell width since they differ by higher-order terms and their relations3506

becomes non-perturbative when the on-shell width becomes of the same order of the on-shell mass3507

(typically, for on-shell masses above800GeV).3508

The CMS can be translated into a more familiar language by introducing the Bar – scheme. Using3509

Eq.(106) with the parametrization of Eq.(107) we perform the transformation3510

M2H = µ2H + γ2H µH γH =MH ΓH. (134)

It follows the remarkable identity:3511

1

s− sH=(1 + i

ΓH

MH

)(s−M

2H + i

ΓH

MH

s)−1

, (135)

showing that the Bar-scheme is equivalent to introducing a running width in the propagator with param-3512

eters that are not the on-shell ones. Special attention goesto the numerator in Eq.(135) which is essential3513

in providing the right asymptotic behavior whens → ∞, as needed for cancellations with contact terms3514

in VV scattering. A sample of numerical results is shown in Table 60 where we compare the Higgs boson3515

complex pole to the corresponding quantities in the Bar-scheme.3516

The use of the complex pole is recommended even if the accuracy at which its imaginary part can3517

be computed is not of the same quality as the NLO accuracy of the on-shell width. Nevertheless the use3518

November 18, 2011 – 11 : 26 DRAFT 176

of a solid prediction (from a theoretical point of view) should always be preferred to the introduction of3519

ill-defined quantities.3520

We are now in a position to give a more detailed description ofthe strategy behind Eq.(120).3521

Consider the complete amplitude for a given process, e.g., the one in Figure 91; let(s = zs, . . .) the the3522

full list of Mandelstam invariants characterizing the process, then3523

A (s, . . .) = Vprod(s, . . .) ∆prop(s)Vdec(s) +N (s, . . .) . (136)

HereVprod denotes the amplitude for production, e.g.,gg → H(s) + X, ∆prop(s) is the propagation3524

function,Vdec(s) is the amplitude for decay, e.g.,.H(s) → 4 f . If no attempt is made to splitA(s) no3525

ambiguity arises but, usually, the two components are knownat different orders. Ho to define the signal?3526

The following schemes are available:3527

ONBW

S (s, . . .) = Vprod

(µ2H, . . .

)∆prop(s)Vdec(µ

2H) ∆prop(s) = Breit–Wigner. (137)

in general violates gauge invariance, neglects the Higgs off-shellness and introduces the ad hoc3528

Breit–Wigner of Eq.(132).3529

OFFBWS (s, . . .) = Vprod(s, . . .) ∆prop(s)Vdec(s), ∆prop(s) = Breit–Wigner, (138)

in general violates gauge invariance, and introduces an ad hoc Breit–Wigner.3530

ONPS (s, . . .) = Vprod

(µ2H, . . .

)∆prop(s)Vdec(µ

2H), ∆prop(s) = propagator (139)

in general violates gauge invariance and neglects the Higgsoff-shellness.3531

OFFPS (s, . . .) = Vprod(s, . . .) ∆prop(s)Vdec(s), ∆prop(s) = propagator, (140)

in general violates gauge invariance3532

CPPS (s, . . .) = Vprod

(sH, . . .

)∆prop(s)Vdec(sH), ∆prop(s) = propagator, (141)

Only the pole, the residue and the reminder ofA(s) are gauge invariant. Furthermore the CPP-3533

scheme allows to identify POs like the production cross-section and any partial decay width by3534

putting in one-to-one correspondence robust theoretical quantities and experimental data.3535

From the list above it follows that only CPP-scheme should beused, once the S/B interference becomes3536

available. However, the largest part of the available calculations is not yet equipped with Feynman3537

integrals on the second Riemann sheet; furthermore the largest corrections in the production are from3538

QCD and we could argue that gauge invariance is not an issue over there, so that the OFFP-scheme3539

remains, at the moment, the most pragmatic alternative.3540

Implementation of the CPP-scheme requires some care in the presence of four-leg processes (or3541

more). The natural choice is to perform analytical continuation from real kinematics to complex in-3542

variants; consider, for instance, the processgg → Hj where the externalH leg is continued from real3543

on-shell mass tosH. For the three invariants we use the following continuation:3544

t = − s

2

[1− sH

s−(1− 4

sH

s

)1/2cos θ

]

u = − s

2

[1− sH

s+(1− 4

sH

s

)1/2cos θ

], (142)

whereθ is the scattering angle ands = 4E2, where2E is the c.m.s. energy. To summarize, our proposal3545

aims to support the use of Eq.(127) for producing accurate predictions for the Higgs lineshape in the SM;3546

November 18, 2011 – 11 : 26 DRAFT 177

Eq.(127) can be adapted easily for a large class of extensions of the SM. Similarly Eq.(130) should be3547

used to define the Higgs production cross-section instead ofσOS or σOFS of Eq.(131).3548

To repeat an obvious argument the zero-width approximationfor the Higgs boson is usually re-3549

ported in comparing experimental studies and theoretical predictions. The approximation has very low3550

quality in the high-mass region where the Higgs boson has a non negligible width. An integration over3551

some distribution is a more accurate estimate of the signal cross-section and we claim that this distribu-3552

tion should be given by the complex propagator and not by somead hoc Breit–Wigner.3553

As we have already mentioned most of this Section is devoted to studying the Higgs boson line-3554

shape in the high-mass region. However, nothing in the formalism is peculiar to that application and3555

the formalism itself forms the basis for extracting pseudo-observables from experimental data. This is a3556

timely contribution to the relevant literature.3557

Before presenting detailed numerical results and comparisons we give the complete definition of3558

the production cross-section,3559

σprod =∑

i,j

∫PDF ⊗ σ

prodij→all =

∑

i,j

∫ 1

z0

dz

∫ 1

z

dv

vLij(v)σ

propij→all(zs, vs, µR, µF), (143)

wherez0 is a lower bound on the invariant mass of theH decay products, the luminosity is defined by3560

Lij(v) =

∫ 1

v

dx

xfi (x, µF) fj

(vx, µF

), (144)

wherefi is a parton distribution function and3561

σpropij→all(zs, vs, µR, µF) = σij→H+X(zs, vs, µR, µF)

vzs2∣∣∣zs− sH

∣∣∣2

ΓtotH (zs)√zs

. (145)

Therefore,σij→H+X(zs, vs, µR) is the cross section for two partons of invariant massvs (z ≤ v ≤ 1) to3562

produce a final state containing aH of virtuality zs plus jets (X); it is made of several terms3563

∑

ij

σij→H+X(zs, vs, µR, µF) = σgg→H δ(1 −z

v) + σgg→Hg + σqg→Hq + σqq→Hg + NNLO. (146)

As a technical remark the complete phase space integral for the processpi + pj → pk + {f} (pi = xi pi3564

etc.) is written as3565

∫dΦij→f =

∫d4pk δ

+(p2k)∏

l=1,n

d4ql δ+(q2l ) δ

4

(pi + pj − pk −

∑

l

ql

)

=

∫d4kd4Qδ+(p2k) δ

4 (pi + pj − pk −Q)

∫ ∏

l=1,n

d4ql δ+(q2l ) δ

4

(Q−

∑

l

ql

)

=

∫dΦprod

∫dΦdec, (147)

where∫dΦdec is the phase-space for the processQ→ {f} and3566

∫dΦprod = s

∫dz


(Q2 − zs

)θ(Q0) δ

4 (pi + pj − pk −Q)

= s2∫dzdvdt


(Q2 − zs

)θ(Q0) δ

4 (pi + pj − pk −Q)

× δ((pi + pj)

2 − vs)δ((pi +Q)2 − t

). (148)

November 18, 2011 – 11 : 26 DRAFT 178

Eqs.(143) and (145) follow folding with PDFs of argumentxi andxj, after usingxi = x, xj = v/x3567

and after integration overt. At NNLO there is an additional parton in the final state and five invariants3568

are need to describe the partonic process, plus theH virtuality. However, one should remember that at3569

NNLO use is made of the effective theory approximation wherethe Higgs-gluon interaction is described3570

by a local operator. Our variablesz, v are related to POWHEG parametrization [104],Y, ξ, by Y =3571

ln(x/sqrtz) andv = z/(1 − ξ).3572


In the following we will present numerical results obtainedwith the program HTO (G. Passarino, un-3574

published) that allows for the study of the Higgs–boson-lineshape using complex poles. HTO is a FOR-3575

TRAN 95 program that contains a translation of the subroutineHIGGSNNLO written by M. Grazzini for3576

computing the total (on-shell) cross-section for Higgs boson production at NLO and NNLO.3577

The following acronyms will be used:3578

FW Breit–Wigner Fixed Width (Eq.(133))3579

RW Breit–Wigner Running Width (Eq.(132))3580

OS parameters in the On-Shell scheme3581

Bar parameters in Bar-scheme (Eq.(134))3582

FS QCD renormalization (factorization) scales fixed3583

RS QCD renormalization (factorization) scales running3584

All results in this Section refer to√s = 7 TeV and are based on the MSTW2008 PDF sets [95]. The3585

integrand in Eq.(143) has several peaks; the most evident isin the propagator and in HTO a change of3586

variable is performed,3587

zs =1

1 + (µH/γH)2

[µ2H + µH γH tan

(µHγH z

′)],

z′ =s

µHγH

[(am + aM) ζ − am

], am = arctan

µ2H − z0s

µHγH, aM = arctan

s− µ2H

µHγH. (149)

Similarly, another change is performed3588

v = exp{(1− u2

)ln z}, x = exp{

(1− y2

)ln v}. (150)

In comparing the OFFBW-scheme with the OFFP-scheme one should realize that there are two sources3589

of difference, the functional form of the distributions andthe different numerical values of the parameters3590

in the distributions. To understand the impact of the functional form we have performed a comparison3591

where (unrealistically)γH = ΓOSH is used in the Higgs propagator; results are shown in Table 61.3592

In Table 62 we compare the on-shell production cross-section as given in Ref. [6] with the off-shell3593

cross-section in the OFFBW-scheme (Eq.(138)) and in the OFFP-scheme (Eq.(140)).3594

An important question regarding the numerical impact of a calculation where the on-shell Higgs3595

boson is left off-shell and convoluted with some distribution is how much of the effect survives the inclu-3596

sion of theoretical uncertainties. In the OFFBW-scheme we can compare with the results of Ref. [326],3597

at least for values of the Higgs boson mass below300 GeV. We compare with Tabs.2−3 of Ref. [6]3598

at 300GeV and obtain the results shown in Table 63 where only the QCDscale uncertainty is included.3599

At these values of the Higgs boson mass on-shell production and off-shell production sampled over a3600

Breit–Wigner are compatible within the errors. The OFFP-scheme gives a slightly higher central value3601

of 2.86 pb. The comparison shows drastically different results forhigh values of the mass where the3602

difference in central values is much bigger than the theoretical uncertainty.3603

November 18, 2011 – 11 : 26 DRAFT 179

Table 61: The re-weighting factorξ for the (total) integrated Higgs lineshape,σprop/σBW usingγH = ΓOSH in

Eq.(130).

µH [ GeV] ΓOSH [ GeV] σOS [ pb] σBW [ pb] σprop [ pb] ξ

200 1.43 5.249 5.674 5.459 0.962300 8.43 2.418 2.724 2.585 0.949400 29.2 2.035 1.998 1.927 0.964500 68.0 0.8497 0.8108 0.7827 0.965600 123.0 0.3275 0.3231 0.3073 0.951

Table 62: Comparison of the on-shell production cross-section as given in Ref. [6] with the off-shell cross-sectionin the OFFBW-scheme (Eq.(138)) and in the OFFP-scheme (Eq.(140)).

µH[ GeV] ΓOSH [ GeV] γH[ GeV] σOS[ pb] σBW[ pb] σprop[ pb]

500 68.0 60.2 0.8497 0.8239 0.9367550 93.1 82.8 0.5259 0.5161 0.5912600 123 109 0.3275 0.3287 0.3784650 158 139 0.2064 0.2154 0.2482700 199 174 0.1320 0.1456 0.1677750 248 205 0.0859 0.1013 0.1171800 304 245 0.0567 0.0733 0.0850850 371 277 0.0379 0.0545 0.0643900 449 331 0.0256 0.0417 0.0509

Table 63: The production cross-section in pb at300 GeV. Result from HTO is computed with running QCDscales.

Tab. 2 of Ref. [6] Tab. 3 of Ref. [6] Tab. 5 of Ref. [326] HTO RS-option

2.42+0.14−0.15 2.45+0.16

−0.22 2.57+0.15−0.22 2.81+0.25

−0.23

November 18, 2011 – 11 : 26 DRAFT 180

Table 64: Comparison of the production cross-section in the OFFBW-scheme betweenIHIXS (Table 5 ofRef. [326]) and our calculation.∆ is the percentage error due to QCD scales andδ is the percentage ratioHTO/IHIXS.

µH[ GeV] σiHixs[ pb] ∆iHixs[%] σHTO[ pb] ∆HTO[%] δ[%]

200 5.57 +7.19 −9.06 5.63 +9.12 −9.30 1.08220 4.54 +6.92 −8.99 4.63 +8.93 −8.85 1.98240 3.80 +6.68 −8.91 3.91 +8.76 −8.51 2.89260 3.25 +6.44 −8.84 3.37 +8.61 −8.22 3.69280 2.85 +6.18 −8.74 2.97 +8.49 −7.98 4.21300 2.57 +5.89 −8.58 2.69 +8.36 −7.75 4.67

Table 65: Scaling factor OFFP/OFFBW schemes (Eqs.(140) and (138)) for the invariant mass windows ofEq.(152).

µH[ GeV] n = −4 n = −3 n = −2 n = −1 n = 0 n = 1 n = 2 n = 3

500 1.24 1.13 1.08 1.23 1.32 1.11 0.97 0.88600 1.39 1.20 1.08 1.27 1.40 1.12 0.94 0.84650 1.50 1.24 1.08 1.30 1.44 1.13 0.93 0.81700 1.62 1.28 1.09 1.34 1.49 1.13 0.92 0.79750 1.78 1.34 1.10 1.41 1.57 1.14 0.90 0.77800 1.99 1.41 1.12 1.49 1.64 1.14 0.89 0.75

In Table 64 we show a more detailed comparison of the production cross-section in the OFFBW-3604

scheme betweenIHIXS of Ref. [326] and our calculation.∆ is the percentage error due to QCD scales3605

andδ is the percentage ratio HTO/IHIXS.3606

Another quantity that is useful in describing the lineshapeis obtained by introducing3607

M2peak=

(MOS

H

)2+(ΓOSH

)2, (151)

an by considering windows in the invariant mass,3608

[Mpeak+

n

2ΓOSH , Mpeak+

n+ 1

2ΓOSH

], n = 0,±1, . . . . (152)

In Table 65 we present the ratio OFFP/OFFBW for the invariantmass distribution in the windows of3609

Eq.(152).3610

In Table 66 we include uncertainties in the comparison; bothOFFBW and OFFP are computed3611

with the RS option, i.e., running QCD scales instead of a fixedone. Note that forσ(µ) we define a central3612

valueσc = σ(µ) and a scale error as[σ− , σ+] where3613

σ− = minµ∈[µ/2,2µ]

σ(µ), σ+ = maxµ∈[µ/2,2µ]

σ(µ), (153)

November 18, 2011 – 11 : 26 DRAFT 181

Table 66: Production cross section with errors due to QCD scale variation and PDF uncertainty. First entry is theon-shell cross-section of Table 2 of Ref. [6], second entry is OFFBW (Eq.(138)), last entry is OFFP Eq.(140).

µH[ GeV] σ[ pb] Scale [%] PDF [%]

600 0.336 +6.1 − 5.2 +6.2 − 5.30.329 +11.2 − 11.3 +4.7 − 4.80.378 +9.7 − 10.0 +5.0 − 3.9

650 0.212 +6.2 − 5.2 +6.5 − 5.50.215 +12.4 − 12.2 +5.1 − 5.30.248 +10.2 − 10.0 +5.3 − 4.2

700 0.136 +6.3 − 5.3 +6.9 − 5.80.146 +13.9 − 13.3 +5.6 − 5.80.168 +11.0 − 11.1 +5.5 − 4.6

750 0.0889 +6.4 − 5.4 +7.2 − 6.10.101 +15.8 − 14.5 +6.1 − 6.30.117 +12.2 − 11.9 +5.8 − 5.1

800 0.0588 +6.5 − 5.4 +7.6 − 6.30.0733 +18.0 − 16.0 +6.7 − 6.90.0850 +13.7 − 13.0 +6.1 − 5.5

850 0.0394 +6.5 − 5.5 +8.0 − 6.60.0545 +20.4 − 17.6 +7.2 − 7.50.0643 +15.7 − 14.3 +6.5 − 6.0

900 0.0267 +6.7 − 5.6 +8.3 − 6.90.0417 +22.8 − 19.1 +7.7 − 8.00.0509 +18.1 − 16.0 +7.0 − 6.6

and whereµ = µR = µF andµ is the reference scale, static or dynamic.3614

In Table 67 we compare results from Table 5 of Ref. [326] with our OFFBW results with two3615

options: 1)µR, µF are fixed, 2) they run withv/2. For three values ofµH reported we find differences3616

of 2.0%, 3.7% and4.7%, compatible with the scale uncertainty. Furthermore, we use Ref. [6] for input3617

parameters which differ slightly from the one used in Ref. [326]. Note that also the functional form ot3618

the Breit–Wigner is different since their default value is not the one in Eq.(132) but3619

BW(s) =1

π

√sΓH(

√s)

(s− µ2H

)2+ µ2H Γ2

H(µH), (154)

whereΓH(√s) id the decay width of a Higgs boson at rest with mass

√s.3620

In Table 68 we use the OFFP-scheme of Eq.(140) and look for theeffect of running QCD scales3621

in theH invariant mass distribution. Differences are of the order of 2−3% apart from the high-mass side3622

of the distribution for very highH masses. As we mentioned already, the only scheme respectinggauge3623

invariance that allows us for a proper definition of pseudo-observables is the CPP-scheme of Eq.(141). It3624

requires analytical continuation of the Feynman integralsinto the second Riemann sheet. Once again, the3625

definition of POs is conventional but should put in one-to-one correspondence well-defined theoretical3626

predictions with derived experimental data. In Table 69 we give a simple example by considering the3627

November 18, 2011 – 11 : 26 DRAFT 182

Table 67: Comparison of results from Table 5 of Ref. [326] with our OFFBW results (Eq.(138)) with two options:1) µR, µF are fixed, 2) they run withv/2.

IX IS HTOµH[ GeV] σ[ pb] Scale [%] σ1[ pb] Scale [%] σ2[ pb] Scale [%]

220 4.54 +6.9 − 9.0 4.63 +8.9 − 8.9 4.74 +7.3 − 8.7260 3.25 +6.4 − 8.8 3.37 +8.6 − 8.2 3.49 +7.9 − 8.6300 2.57 +5.9 − 8.6 2.69 +8.4 − 7.8 2.81 +8.4 − 8.5

Table 68: Scaling factor in the OFFP-scheme (Eq.(140)) running/fixedQCD scales for the invariant mass distri-bution. Here[x, y] = [Mpeak+ xΓOS

H , Mpeak+ y ΓOSH ].

µH[ GeV] [−1 , −12 ] [−1

2 , −14 ] [−1

4 , 0] [0 , 14 ] [14 ,

12 ] [12 , 1]

600 1.023 1.021 1.019 1.018 1.017 1.016700 1.027 1.023 1.021 1.019 1.018 1.019800 1.030 1.024 1.021 1.021 1.021 1.136

processgg → H at lowest order and compare the traditional on-shell production cross-section, see the3628

l.h.s. of Eq.(131), with the production cross-section as defined in the CPP-scheme. Therefore we only3629

considergg → H at LO (i.e.,v = z) and putH on its real mass-shell or on the complex one. Below3630

300 GeV there is no visible difference, at300 GeV the two results start to differ with an increasing gap3631

up to600 GeV after which there is a plateau of about25% for higher values ofµH.3632

The production cross-section in Eq.(146) is made of one termcorresponding togg → H which3633

we denote byσ0 and terms with at least one additional jet,σj . The invariant mass of the two partons in3634

the initial state isvs with z ≤ v ≤ 1, zs being the Higgs virtuality. in Table 70 we introduce a cut such3635

that3636

z ≤ v ≤ min{vc z , 1} (155)

and study the dependence of the result onvc by consideringσt = σ0 + σj andδ = σtc/σt. The results3637

show that a cutz ≤ v ≤ 1.01 z gives already85% of the total answer.3638

In Figure 85 we compare the production cross-section as computed with the OFFP-scheme of3639

Eq.(140) or with the OFFBW-scheme of Eq.(138). For the latter we use Breit–Wigner parameters in the3640

OS-scheme (red curve) and in the Bar-scheme of Eq.(134) (blue curve).3641

In Figure 86 we show the effect of using dynamical QCD scales for the production cross-section,3642

In Figure 87 we consider the on-shell production cross-section σOS(pp → H) (black curve) which3643

includes convolution with PDFs. The blue curve gives the off-shell production cross-section sampled3644

over the (complex) Higgs propagator while the red curves is sampled over a Breit–Wigner distribution.3645

In Figure 88 we show the differentialK factor for the processpp → (H → 4 e) + X, comparing3646

the fixed scale option,µR = µF =MH/2, and the running scale option,µR = µF =M(4 e)/2.3647

November 18, 2011 – 11 : 26 DRAFT 183

Table 69: γH andΓOSH as a function ofµH. We also report the ratio bewteen the LO cross-sections forgg → H in

the CPP-scheme and in the OS-scheme.

µH[ GeV] γH[ GeV] ΓOSH [ GeV] σCPP(sH) /σOS(M

OSH )

300 7.58 8.43 0.999350 14.93 15.20 1.086400 26.66 29.20 1.155450 41.18 46.90 1.183500 58.85 68.00 1.204550 79.80 93.10 1.221600 104.16 123.00 1.236650 131.98 158.00 1.248700 163.26 199.00 1.256750 197.96 248.00 1.262800 235.93 304.00 1.264850 277.00 371.00 1.263900 320.96 449.00 1.258950 367.57 540.00 1.252

1000 416.57 647.00 1.242

Table 70: The effect of introducing a cut on the invariant mass of the initial-state partons.

µH[ GeV] vc σ0[ pb] σj [ pb] σt[ pb] δ[%]

600 no cut 0.2677 0.1107 0.37841.001 0.0127 0.2804 741.01 0.0473 0.3149 831.05 0.0918 0.3595 95

700 no cut 0.1208 0.0469 0.16771.001 0.0054 0.1262 751.01 0.0201 0.1409 841.05 0.0391 0.1599 95

800 no cut 0.0632 0.0218 0.08501.001 0.0025 0.0657 771.01 0.0094 0.0726 851.05 0.0182 0.0814 96

November 18, 2011 – 11 : 26 DRAFT 184

In Figure 89 we show the normalized invariant mass distribution in the OFFP-scheme with running3648

QCD scales for600 GeV (black),700 GeV (blue),800 GeV (red) in the windowsMpeak± 2ΓOS where3649

Mpeak is defined in Eq.(151).3650

Finally, Figure 90 we show the normalized invariant mass distribution in the OFFP-scheme (blue)3651

and OFFBW-scheme (red) with running QCD scales at800 GeV in the windowMpeak± 2ΓOS.3652

15.5 QCD scale error3653

The conventional theoretical uncertainty associated withQCD scale variation is defined in Eq.(153). Let3654

us consider the production cross-section at800 GeV in the OFFP-scheme with running or fixed QCD3655

scales, we obtain3656

RS 0.08497+13.7%−13.0%, FS 0.07185+6.7%

−8.5%. (156)

The uncertainty with running scales is about twice the one where the scales are kept fixed. One might3657

wonder which is the major source and we have done the following; in estimating the conventional uncer-3658

tainty in the RS-option we keepµF = µ = v/2 and varyµR betweenµ/2 and2µ. The corresponding3659

result is3660

RS 0.08497+3.9%−4.4%, µR only. (157)

Therefore, the main source of uncertainty comes from varying the factorization scale. However, in the3661

fixed-scale option we obtain3662

FS 0.07185+3.6%−4.4%, µR only (158)

andµF -variation is less dominant. In any case the question of which variation is dominating depends on3663

the mass-range; indeed, in the ONBW-scheme with fixed scalesat140 GeV we have3664

ONBW 12.27 +11.1%−10.1%, µR and µF

ONBW 12.27 +8.7%−9.6%, µR only (159)

showingµR dominance.3665

In order to compare this conventional definition of uncertainty with the work of Ref. [339] we3666

recall their definition ofp% credible interval; given a series3667

σ =

k∑

n=l

cn αns , (160)

thep% credible intervalσ ±∆σp is defined as3668

∆σp = αk+1s max ({c}) nc + 1

ncp%, p% ≤ nc

nc + 1,

∆σp = αk+1s max ({c})

[(nc + 1) (1 − p%)

]−1/nc

, p% ≥ ncnc + 1

, (161)

with nc = k− l+1. Using this definition we find that the68%(90%) credible interval forµR uncertainty3669

in the production cross-section at800 GeV is3.1%(5.3%) in substantial agreement with the conventional3670

method. For ONBW-scheme at140 GeV the90% credible interval forµR uncertainty is8.0%. It could3671

be interesting to extend the method of Ref. [339] to coverµF uncertainty.3672

November 18, 2011 – 11 : 26 DRAFT 185

15.6 Conclusions3673

In the last two decades many theoretical studies lead to improved estimates of the SM Higss boson3674

total cross section at hadron colliders [63, 141, 147, 153, 340, 341] and of Higgs boson partial decay3675

widths [17]. Less work has been devoted to studying the Higgsboson invariant mass distribution (Higgs–3676

boson-lineshape).3677

In this Section we made an attempt to resolve the problem by comparing different theoretical inputs3678

to the off-shellness of the Higgs boson. There is no questionat all that the zero-width approximation3679

should be avoided, especially in the high-mass region wherethe on-shell width becomes of the same3680

order as the on-shell mass.3681

The propagation of the off-shellH is usually parametrized in terms of some Breit-Wigner distri-3682

bution (several variants are reported in the literature, Eq.(132) and Eq.(154)); we have shown evidence3683

that only the Dyson-resummed propagator should be used, leading to the introduction of theH complex3684

pole, a gauge-invariant property of theS -matrix.3685

Finally, when one accepts the idea that the Higgs boson is an off-shell intermediate state the3686

question of the most appropriate choice of QCD scales arises. We have shown the effect of including3687

dynamical choices forµR, µF instead of a static choice.3688

For many purposes the well-known and convenient machinery of the on-shell approach can be3689

employed but one should become aware of its limitations and potential pitfalls. Although the basic3690

comparison between different schemes was presented in thisSection, at this time we are repeating that3691

differences should not be taken as the source of additional theoretical uncertainty; as a consequence, our3692

recommendation is to use the OFFP-scheme described in this Section (see Eq.(140)) with running QCD3693

scales.3694

November 18, 2011 – 11 : 26 DRAFT 186

Higgs virtuality [ GeV]

pro

pag

ator

/B

reit

–Wig

ner

−1

[%]

−20

−10

0

+10

+20

+30

+40

µH − 200 µH µH + 200

µH = 600 GeV

Bar – scheme

OFFBW – scheme

MH = 608.6 GeV

ΓH = 100.7 GeVΓOS

H = 113.9 GeV

©HTO

Fig. 85: Comparison of production cross-section as computed with the OFFP-scheme of Eq.(140) or with theOFFBW-scheme of Eq.(138). The red curve gives Breit–Wignerparameters in the OS-scheme and the blue one inthe Bar-scheme of Eq.(134).

November 18, 2011 – 11 : 26 DRAFT 187


runnin

gsc

ale

/fixed

scal

e−

1[%

]

−3

−2

−1

0

+1

+2

+3

µH − 100 µH µH + 100

µH = 400 GeV

gg → H + X → γγ+ X

RS → µR = µF = M(γγ)/2

FS → µR = µF = µH/2

©HTO

Fig. 86: The effect of using dynamical QCD scales for the production cross-section of Eqs.(143)–(145).

November 18, 2011 – 11 : 26 DRAFT 188

µH [ GeV]

opti

on/

OS

-pro

duct

ion−

1[%

]

σO

S

pro

d[pb]

170 230 2901

3

5

7

9

11

13

15

2

4

6

8©HTO

Fig. 87: The on-shell production cross-section (black curve). The blue curve gives the off-shell production cross-section sampled over the (complex) Higgs propagator while the red curves is sampled over a Breit–Wigner distri-bution (see Eq.(132)).

November 18, 2011 – 11 : 26 DRAFT 189


diff

eren

tial

K–

fact

ors

RS → µR = µF = M(4 e)/2

FS → µR = µF = µH/2

1.0

1.5

2.0

400 600 800

µH = 600 GeV

NNLO/LO RS

NLO/LO RS

NNLO/LO FS

NLO/LO FS

gg → H + X → 4 e + X

©HTO

Fig. 88: DifferentialK factor for the processpp → (H → 4 e)+X, comparing the fixed scale option,µR = µF =

MH/2, and the running scale option,µR = µF =M(4 e)/2.

November 18, 2011 – 11 : 26 DRAFT 190

200 400 600 800 1000 1200 1400

0.00

0.01

0.02

0.03

0.04

0.05

M [ GeV]

M2

σdσ

dM

2

Fig. 89: The normalized invariant mass distribution in the OFFP-scheme with running QCD scales for600 GeV(black),700 GeV (blue),800 GeV (red) in the windowsMpeak± 2 ΓOS.

November 18, 2011 – 11 : 26 DRAFT 191

200 400 600 800 1000 1200 1400

0.00

0.01

0.02

0.03

0.04

0.05

M [ GeV]

M2

σdσ

dM

2

Fig. 90: The normalized invariant mass distribution in the OFFP-scheme (blue) and OFFBW-scheme (red) withrunning QCD scales at800 GeV in the windowMpeak± 2 ΓOS.

November 18, 2011 – 11 : 26 DRAFT 192

i

j

k

v s =⇒ z s =⇒f

Vprop(vs , zs , t) Vdec(z s)

H

∆(z s)

t ց

=⇒ σij→H+k(vs , t , zs)vzs2

∣

∣

∣zs − sH

∣

∣

∣

2

ΓH→f(zs)

(zs)1/2+ NR

= σij→H+k(vs , t , sH)vs

∣

∣

∣sH

∣

∣

∣

1/2

∣

∣

∣zs − sH

∣

∣

∣

2 ΓH→f(sH) + NR′

Fig. 91: The resonant part of the processij → H+k wherei, j andk are partons (g orq). We distinguish betweenproduction, propagation and decay, indicating the explicit dependence on Mandelstam invariants. Ifs denotes thepp invariant mass we distinguish betweenvs, theij invariant mass,zs, the Higgs boson virtuality andt which isrelated to the Higgs boson transverse momentum. Within NR weinclude the Non-Resonant contributions as wellas their interference with the signal. NR’ includes those terms that are of higher order in the Laurent expansion ofthe signal around the complex pole. At NNLO QCD the partonk is a pairk1−k2 and more invariants are neededto characterize the production mechanism.

November 18, 2011 – 11 : 26 DRAFT 193

Acknowledgements3695

We are obliged to ... for their support and encouragement.3696

We would like to acknowledge the assistance of ...3697

We would like to thank ... for discussions.3698

We are obliged to CERN, in particular to the IT Department andto the Theory Unit for the support3699

with logistics, especially to Elena Gianolio for technicalassistance.3700

We also acknowledge partial support from the European Community’s Marie-Curie Research3701

Training Network under contract MRTN-CT-2006-035505 ‘Tools and Precision Calculations for Physics3702

Discoveries at Colliders’, from the Science and TechnologyFacilities Council, from the US Depart-3703

ment of Energy, and from the Forschungsschwerpunkt 101 by the Bundesministerium für Bildung und3704

Forschung, Germany.3705

O. Brein and M. Warsinsky acknowledge the support of the Initiative and Networking Fund of the3706

Helmholtz Association, contract HA-101 (‘Physics at the Terascale’).3707

References3708

[1] P. W. Higgs,Broken symmetries, massless particles and gauge fields, Phys. Lett.12 (1964)3709

132–133.3710

[2] P. W. Higgs,Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett.13 (1964)3711

508–509.3712

[3] P. W. Higgs,Spontaneous symmetry breakdown without massless bosons, Phys. Rev.145(1966)3713

1156–1163.3714

[4] F. Englert and R. Brout,Broken symmetry and the mass of gauge vector mesons, Phys. Rev. Lett.3715

13 (1964) 321–323.3716

[5] G. Guralnik, C. Hagen, and T. Kibble,Global conservation laws and massless particles, Phys.3717

Rev. Lett.13 (1964) 585–587.3718

[6] LHC Higgs Cross Section Working Group Collaboration, S.Dittmaier et al.,Handbook of LHC3719

Higgs Cross Sections: 1. Inclusive Observables, arXiv:1101.0593 [hep-ph].3720

[7] M. S. Carena, S. Heinemeyer, C. E. M. Wagner, and G. Weiglein, Suggestions for benchmark3721

scenarios for MSSM Higgs boson searches at hadron colliders, Eur. Phys. J.C26 (2003)3722

601–607,arXiv:hep-ph/0202167.3723

[8] The ATLAS Collaboration Collaboration, G. Aad et al.,Expected Performance of the ATLAS3724

Experiment - Detector, Trigger and Physics, arXiv:0901.0512 [hep-ex].3725

[9] CMS Collaboration, G. L. Bayatian et al.,CMS technical design report, volume II: Physics3726

performance, J. Phys.G34 (2007) 995–1579.3727

[10] M. Dührssen et al.,Extracting Higgs boson couplings from LHC data, Phys. Rev.D70 (2004)3728

113009,arXiv:hep-ph/0406323.3729

[11] A. Denner, S. Heinemeyer, I. Puljak, D. Rebuzzi, and M. Spira,Standard Model Higgs-Boson3730

Branching Ratios with Uncertainties, Eur.Phys.J.C71 (2011) 1753,arXiv:1107.59093731

[hep-ph].3732

[12] A. Djouadi, J. Kalinowski, and M. Spira,HDECAY: A program for Higgs boson decays in the3733

standard model and its supersymmetric extension, Comput. Phys. Commun.108(1998) 56–74,3734

arXiv:hep-ph/9704448.3735

[13] M. Spira,QCD effects in Higgs physics, Fortschr. Phys.46 (1998) 203–284,3736


November 18, 2011 – 11 : 26 DRAFT 194

[14] A. Djouadi, J. Kalinowski, M. Mühlleitner, and M. Spira, An update of the program HDECAY, in3738

The Les Houches 2009 workshop on TeV colliders: The tools andMonte Carlo working group3739

summary report. 2010.arXiv:1003.1643 [hep-ph].3740

[15] A. Bredenstein, A. Denner, S. Dittmaier, and M. M. Weber, Precise predictions for the3741

Higgs-boson decay H→ WW/ZZ→ 4 leptons, Phys. Rev.D74 (2006) 013004,3742


[16] A. Bredenstein, A. Denner, S. Dittmaier, and M. Weber,Radiative corrections to the semileptonic3744

and hadronic Higgs-boson decays H→W W / Z Z→ 4 fermions, JHEP0702(2007) 080,3745

arXiv:hep-ph/0611234 [hep-ph].3746

[17] A. Bredenstein, A. Denner, S. Dittmaier, A. Mück, and M.M. Weber,Prophecy4f: A Monte3747

Carlo generator for a proper description of the Higgs decay into 4 fermions,3748

http://omnibus.uni-freiburg.de/~sd565/programs/prophecy4f/prophecy4f.html,3749

2010.3750

[18] A. Ghinculov,Two loop heavy Higgs correction to Higgs decay into vector bosons, Nucl. Phys.3751

B455(1995) 21–38,arXiv:hep-ph/9507240 [hep-ph].3752

[19] A. Frink, B. A. Kniehl, D. Kreimer, and K. Riesselmann,Heavy Higgs lifetime at two loops,3753

Phys. Rev.D54 (1996) 4548–4560,arXiv:hep-ph/9606310 [hep-ph].3754

[20] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini,Master integrals for the two-loop light3755

fermion contributions to gg→ H and H→ γγ, Phys. Lett.B600(2004) 57–64,3756


[21] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini,Two-loop light fermion contribution to3758

Higgs production and decays, Phys. Lett.B595(2004) 432–441,arXiv:hep-ph/0404071.3759

[22] U. Aglietti et al.,Tevatron for LHC report: Higgs, arXiv:hep-ph/0612172.3760

[23] G. Degrassi and F. Maltoni,Two-loop electroweak corrections to Higgs production at hadron3761

colliders, Phys. Lett.B600(2004) 255–260,arXiv:hep-ph/0407249.3762

[24] G. Degrassi and F. Maltoni,Two-loop electroweak corrections to the Higgs-boson decayH→ γγ,3763

Nucl. Phys.B724(2005) 183–196,arXiv:hep-ph/0504137.3764

[25] S. Actis, G. Passarino, C. Sturm, and S. Uccirati,NLO electroweak corrections to Higgs boson3765

production at hadron colliders, Phys. Lett.B670(2008) 12–17,arXiv:0809.1301 [hep-ph].3766

[26] S. Actis, G. Passarino, C. Sturm, and S. Uccirati,NNLO computational techniques: the cases3767

H → γγ andH → gg, Nucl. Phys.B811(2009) 182–273,arXiv:0809.3667 [hep-ph].3768

[27] S. Narison,A Fresh look into the heavy quark mass values, Phys.Lett.B341(1994) 73–83,3769


[28] S. Bethke,The 2009 World Average ofαs(MZ), Eur. Phys. J.C64 (2009) 689–703,3771

arXiv:0908.1135 [hep-ph].3772

[29] Particle Data Group Collaboration, K. Nakamura et al.,Review of particle physics, J. Phys.G373773

(2010) 075021.3774

[30] J. H. Kuhn, M. Steinhauser, and C. Sturm,Heavy quark masses from sum rules in four-loop3775

approximation, Nucl. Phys.B778(2007) 192–215,arXiv:hep-ph/0702103.3776

[31] K. Chetyrkin et al.,Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental3777

Uncertainties, arXiv:1010.6157 [hep-ph].3778

[32] A. Signer, private communication.3779

[33] B. Dehnadi, A. H. Hoang, V. Mateu, and S. M. Zebarjad,Charm Mass Determination from QCD3780

Charmonium Sum Rules at Order alpha(s)**3, arXiv:1102.2264 [hep-ph].3781

[34] CDF and D0 Collaboration, and others,Combination of CDF and D0 Results on the Mass of the3782

Top Quark, arXiv:1007.3178 [hep-ex].3783

[35] S. Gorishnii, A. Kataev, S. Larin, and L. Surguladze,Corrected three loop QCD correction to the3784

November 18, 2011 – 11 : 26 DRAFT 195

correlator of the quark scalar current andΓtot(H → hadrons), Mod. Phys. Lett.A5 (1990)3785

2703–2712.3786

[36] S. Gorishnii, A. Kataev, S. Larin, and L. Surguladze,Scheme dependence of the next to3787

next-to-leading QCD corrections toΓtot(H → hadrons) and the spurious QCD infrared fixed3788

point, Phys. Rev.D43 (1991) 1633–1640.3789

[37] A. L. Kataev and V. T. Kim,The effects of the QCD corrections toΓ(H → bb), Mod. Phys. Lett.3790

A9 (1994) 1309–1326. Revised version of ENSLAPP-A-407-92.3791

[38] L. R. Surguladze,Quark mass effects in fermionic decays of the Higgs boson in O(α2s )3792

perturbative QCD, Phys. Lett.B341(1994) 60–72,arXiv:hep-ph/9405325 [hep-ph].3793

[39] S. Larin, T. van Ritbergen, and J. Vermaseren,The large top quark mass expansion for Higgs3794

boson decays into bottom quarks and into gluons, Phys. Lett.B362(1995) 134–140,3795


[40] K. Chetyrkin and A. Kwiatkowski,Second order QCD corrections to scalar and pseudoscalar3797

Higgs decays into massive bottom quarks, Nucl. Phys.B461(1996) 3–18,3798


[41] K. Chetyrkin,Correlator of the quark scalar currents andΓtot(H → hadrons) at O (α3s ) in3800

pQCD, Phys. Lett.B390(1997) 309–317,arXiv:hep-ph/9608318 [hep-ph].3801

[42] P. A. Baikov, K. G. Chetyrkin, and J. H. Kuhn,Scalar correlator at O(alpha(s)**4), Higgs decay3802

into b- quarks and bounds on the light quark masses, Phys. Rev. Lett.96 (2006) 012003,3803


[43] J. Fleischer and F. Jegerlehner,Radiative corrections to Higgs decays in the extended3805

Weinberg-Salam model, Phys. Rev.D23 (1981) 2001–2026.3806

[44] D. Bardin, B. Vilensky, and P. Khristova,Calculation of the Higgs boson decay width into3807

fermion pairs, Sov. J. Nucl. Phys.53 (1991) 152–158.3808

[45] A. Dabelstein and W. Hollik,Electroweak corrections to the fermionic decay width of the3809

standard Higgs boson, Z. Phys.C53 (1992) 507–516.3810

[46] B. A. Kniehl, Radiative corrections for H→ f f (γ) in the standard model, Nucl. Phys.B3763811

(1992) 3–28.3812

[47] A. Djouadi, D. Haidt, B. A. Kniehl, P. M. Zerwas, and B. Mele, Higgs in the standard model, . In3813

*Munich/Annecy/Hamburg 1991, Proceedings, e+ e- collisions at 500-GeV, pt. A* 11-30.3814

[48] E. Braaten and J. P. Leveille,Higgs boson decay and the running mass, Phys. Rev.D22 (1980)3815

715.3816

[49] N. Sakai,Perturbative QCD corrections to the hadronic decay width ofthe Higgs boson, Phys.3817

Rev.D22 (1980) 2220.3818

[50] T. Inami and T. Kubota,Renormalization group estimate of the hadronic decay widthof the3819

Higgs boson, Nucl. Phys.B179(1981) 171.3820

[51] S. Gorishnii, A. Kataev, and S. Larin,The width of Higgs boson decay into hadrons: three loop3821

corrections of strong interactions, Sov. J. Nucl. Phys.40 (1984) 329–334.3822

[52] M. Drees and K.-i. Hikasa,Heavy quark thresholds in Higgs physics, Phys. Rev.D41 (1990)3823

1547.3824

[53] M. Drees and K.-i. Hikasa,Note on QCD corrections to hadronic Higgs decay, Phys. Lett.B2403825

(1990) 455.3826

[54] M. Drees and K.-i. Hikasa,Erratum: Note on QCD corrections to hadronic Higgs decay, Phys.3827

Lett. B262(1991) 497.3828

[55] A. Ghinculov,Two loop heavy Higgs corrections to the Higgs fermionic width, Phys. Lett.B3373829

(1994) 137–140,arXiv:hep-ph/9405394 [hep-ph].3830

[56] A. Ghinculov,Erratum: Two loop heavy Higgs corrections to the Higgs fermionic width, Phys.3831

November 18, 2011 – 11 : 26 DRAFT 196

Lett. B346(1995) 426,arXiv:hep-ph/9405394 [hep-ph].3832

[57] L. Durand, K. Riesselmann, and B. A. Kniehl,Onset of strong interactions in the Higgs sector of3833

the standard model:H → f f at two loops, Phys. Rev. Lett.72 (1994) 2534–2537.3834

[58] L. Durand, K. Riesselmann, and B. A. Kniehl,Erratum:Onset of strong interactions in the Higgs3835

sector of the standard model:H → f f at two loops, Phys. Rev. Lett.74 (1995) 1699.3836

[59] L. Durand, B. A. Kniehl, and K. Riesselmann,Two loop O (G2FM

4H ) corrections to the fermionic3837

decay rates of the Higgs boson, Phys. Rev.D51 (1995) 5007–5015,arXiv:hep-ph/94123113838

[hep-ph].3839

[60] V. Borodulin and G. Jikia,Analytic evaluation of two loop renormalization constantsof enhanced3840

electroweak strength in the Higgs sector of the standard model, Phys. Lett.B391(1997)3841

434–440,arXiv:hep-ph/9609447 [hep-ph].3842

[61] T. Inami, T. Kubota, and Y. Okada,Effective gauge theory and the effect of heavy quarks in Higgs3843

boson decay, Z. Phys.C18 (1983) 69.3844

[62] A. Djouadi, M. Spira, and P. M. Zerwas,Production of Higgs bosons in proton colliders: QCD3845

corrections, Phys. Lett.B264(1991) 440–446.3846

[63] M. Spira, A. Djouadi, D. Graudenz, and P. M. Zerwas,Higgs boson production at the LHC, Nucl.3847

Phys.B453(1995) 17–82,hep-ph/9504378.3848

[64] K. Chetyrkin, B. A. Kniehl, and M. Steinhauser,Hadronic Higgs decay to orderα4s , Phys. Rev.3849

Lett. 79 (1997) 353–356,arXiv:hep-ph/9705240 [hep-ph].3850

[65] P. Baikov and K. Chetyrkin,Higgs decay into hadrons to orderα5s , Phys. Rev. Lett.97 (2006)3851

061803,arXiv:hep-ph/0604194 [hep-ph].3852

[66] H.-Q. Zheng and D.-D. Wu,First order QCD corrections to the decay of the Higgs boson into3853

two photons, Phys. Rev.D42 (1990) 3760–3763.3854

[67] A. Djouadi, M. Spira, J. van der Bij, and P. Zerwas,QCD corrections toγγ decays of Higgs3855

particles in the intermediate mass range, Phys. Lett.B257(1991) 187–190.3856

[68] S. Dawson and R. Kauffman,QCD corrections toH → γγ, Phys. Rev.D47 (1993) 1264–1267.3857

[69] A. Djouadi, M. Spira, and P. Zerwas,Two photon decay widths of Higgs particles, Phys. Lett.3858


[70] K. Melnikov and O. I. Yakovlev,Higgs→ two photon decay: QCD radiative correction, Phys.3860

Lett. B312(1993) 179–183,arXiv:hep-ph/9302281 [hep-ph].3861

[71] M. Inoue, R. Najima, T. Oka, and J. Saito,QCD corrections to two photon decay of the Higgs3862

boson and its reverse process, Mod. Phys. Lett.A9 (1994) 1189–1194.3863

[72] A. Firan and R. Stroynowski,Internal conversions in Higgs decays to two photons, Phys. Rev.3864

D76 (2007) 057301,arXiv:0704.3987 [hep-ph].3865

[73] M. Spira, A. Djouadi, and P. M. Zerwas,QCD corrections to the H Z gamma coupling, Phys.3866

Lett. B276(1992) 350–353.3867

[74] S. Heinemeyer, W. Hollik, and G. Weiglein,FeynHiggs: a program for the calculation of the3868

masses of the neutral CP-even Higgs bosons in the MSSM, Comput. Phys. Commun.124 (2000)3869

76–89,arXiv:hep-ph/9812320.3870

[75] S. Heinemeyer, W. Hollik, and G. Weiglein,The masses of the neutral CP-even Higgs bosons in3871

the MSSM: accurate analysis at the two loop level, Eur. Phys. J.C9 (1999) 343–366,3872


[76] G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, and G. Weiglein,Towards high-precision3874

predictions for the MSSM Higgs sector, Eur. Phys. J.C28 (2003) 133–143,3875


[77] M. Frank et al.,The Higgs boson masses and mixings of the complex MSSM in the3877

Feynman-diagrammatic approach, JHEP02 (2007) 047,arXiv:hep-ph/0611326.3878

November 18, 2011 – 11 : 26 DRAFT 197

[78] J. S. Lee et al.,CPsuperH: a computational tool for Higgs phenomenology in the minimal3879

supersymmetric standard model with explicit CP violation, Comput. Phys. Commun.156(2004)3880

283–317,arXiv:hep-ph/0307377.3881

[79] J. S. Lee, M. Carena, J. Ellis, A. Pilaftsis, and C. E. M. Wagner,CPsuperH2.0: an improved3882

computational tool for Higgs phenomenology in the MSSM withexplicit CP violation, Comput.3883

Phys. Commun.180(2009) 312–331,arXiv:0712.2360 [hep-ph].3884

[80] P. Z. Skands, B. Allanach, H. Baer, C. Balazs, G. Belanger, et al.,SUSY Les Houches accord:3885

Interfacing SUSY spectrum calculators, decay packages, and event generators, JHEP04073886

(2004) 036,arXiv:hep-ph/0311123 [hep-ph].3887

[81] B. Allanach, C. Balazs, G. Belanger, M. Bernhardt, F. Boudjema, et al.,SUSY Les Houches3888

Accord 2, Comput.Phys.Commun.180(2009) 8–25,arXiv:0801.0045 [hep-ph].3889

[82] S. AbdusSalam, B. Allanach, H. Dreiner, J. Ellis, U. Ellwanger, et al.,Benchmark Models,3890

Planes, Lines and Points for Future SUSY Searches at the LHC, arXiv:1109.3859 [hep-ph].3891

[83] D. Noth and M. Spira,Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD3892

corrections, Phys. Rev. Lett.101(2008) 181801,arXiv:0808.0087 [hep-ph].3893

[84] R. D. Ball et al.,Impact of Heavy Quark Masses on Parton Distributions and LHC3894

Phenomenology, Nucl. Phys.B849(2011) 296–363,arXiv:1101.1300 [hep-ph].3895

[85] R. D. Ball et al.,A first unbiased global NLO determination of parton distributions and their3896

uncertainties, Nucl. Phys.B838(2010) 136–206,arXiv:1002.4407 [hep-ph].3897

[86] S. Forte, E. Laenen, P. Nason, and J. Rojo,Heavy quarks in deep-inelastic scattering, Nucl.Phys.3898

B834(2010) 116–162,arXiv:1001.2312 [hep-ph].3899

[87] The NNPDF Collaboration Collaboration, R. D. Ball et al., Unbiased global determination of3900

parton distributions and their uncertainties at NNLO and atLO, Nucl. Phys.in press(2011) ,3901

arXiv:1107.2652 [hep-ph].3902

[88] for the H1 and ZEUS Collaborations Collaboration, A. Cooper-Sarkar,Proton Structure from3903

HERA to LHC, arXiv:1012.1438 [hep-ph].3904

[89] H1 and ZEUS Collaboration, F. D. Aaron et al.,Combined measurement and QCD analysis of3905

the inclusive ep scattering cross sections at HERA, JHEP01 (2010) 109,arXiv:0911.08843906

[hep-ex].3907

[90] M. Botje et al.,The PDF4LHC Working Group Interim Recommendations, arXiv:1101.05383908

[hep-ph].3909

[91] P. M. Nadolsky et al.,Implications of CTEQ global analysis for collider observables, Phys. Rev.3910

D78 (2008) 013004,arXiv:0802.0007 [hep-ph].3911

[92] H.-L. Lai et al.,New parton distributions for collider physics, arXiv:1007.2241 [hep-ph].3912

[93] J. M. Campbell and R. K. Ellis,Radiative corrections to Z b anti-b production, Phys. Rev.D623913

(2000) 114012,arXiv:hep-ph/0006304.3914

[94] J. Campbell and R. K. Ellis,Next-to-leading order corrections to W + 2jet and Z + 2jet3915

production at hadron colliders, Phys. Rev.D65 (2002) 113007,arXiv:hep-ph/0202176.3916

[95] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt,Parton distributions for the LHC, Eur.3917

Phys. J.C63 (2009) 189–285,arXiv:0901.0002 [hep-ph].3918

[96] M. Glück, P. Jimenez-Delgado, and E. Reya,Dynamical parton distributions of the nucleon and3919

very small-x physics, Eur. Phys. J.C53 (2008) 355–366,arXiv:0709.0614 [hep-ph].3920

[97] M. Gluck, P. Jimenez-Delgado, E. Reya, and C. Schuck,On the role of heavy flavor parton3921

distributions at high energy colliders, Phys. Lett.B664(2008) 133–138,arXiv:0801.36183922

[hep-ph].3923

[98] S. Alekhin, J. Blümlein, S. Klein, and S. Moch,The 3-, 4-, and 5-flavor NNLO parton from3924

deep-inelastic-scattering data and at hadron colliders, Phys. Rev.D81 (2010) 014032,3925

November 18, 2011 – 11 : 26 DRAFT 198

arXiv:0908.2766 [hep-ph].3926

[99] F. Demartin, S. Forte, E. Mariani, J. Rojo, and A. Vicini, The impact of PDF andαs uncertainties3927

on Higgs production in gluon fusion at hadron colliders, Phys. Rev.D82 (2010) 014002,3928

arXiv:1004.0962 [hep-ph].3929

[100] PDF Correlation Tables,3930

https://twiki.cern.ch/twiki/bin/view/LHCPhysics/PDFCorrelations.3931

[101] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt,Uncertainties onαs in global PDF3932

analyses and implications for predicted hadronic cross sections, Eur. Phys. J.C64 (2009)3933

653–680,arXiv:0905.3531 [hep-ph].3934

[102] H.-L. Lai et al.,Uncertainty induced by QCD coupling in the CTEQ global analysis of parton3935

distributions, arXiv:1004.4624 [hep-ph].3936

[103] http://theory.fi.infn.it/grazzini/codes.html .3937

[104] S. Alioli, P. Nason, C. Oleari, and E. Re,NLO Higgs boson production via gluon fusion matched3938

with shower in POWHEG, JHEP04 (2009) 002,arXiv:0812.0578 [hep-ph].3939

[105] P. Nason,Recent Developments in POWHEG, PoSRADCOR2009(2010) 018,3940

arXiv:1001.2747 [hep-ph].3941

[106] P. Torrielli and S. Frixione,Matching NLO QCD computations with PYTHIA using MC@NLO,3942

JHEP1004(2010) 110,arXiv:1002.4293 [hep-ph].3943

[107] S. Catani, B. Webber, F. Fiorani, and G. Marchesini,Structure functions at small x and associate3944

radiation, Nucl.Phys.Proc.Suppl.23B (1991) 123–129.3945

[108] E. Bagnaschi, G. Degrassi, P. Slavich, and A. Vicini,Higgs production via gluon fusion in the3946

POWHEG approach in the SM and in the MSSM, arXiv:1111.2854 [hep-ph]. * Temporary3947

entry *.3948

[109] M. Grazzini,NNLO predictions for the Higgs boson signal in the H→WW→ lνlν and3949

H→ZZ→4l decay channels, arXiv:0801.3232 [hep-ph].3950

[110] T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, et al.,Event generation with3951

SHERPA 1.1, JHEP0902(2009) 007,arXiv:0811.4622 [hep-ph].3952

[111] P. Nason,A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP3953

11 (2004) 040,arXiv:hep-ph/0409146.3954

[112] S. Frixione, P. Nason, and C. Oleari,Matching NLO QCD computations with parton shower3955

simulations: the POWHEG method, JHEP11 (2007) 070,arXiv:0709.2092 [hep-ph].3956

[113] S. Frixione and B. R. Webber,Matching NLO QCD computations and parton shower3957

simulations, JHEP06 (2002) 029,arXiv:hep-ph/0204244.3958

[114] S. Hoche, F. Krauss, M. Schonherr, and F. Siegert,Automating the POWHEG method in Sherpa,3959

JHEP1104(2011) 024,arXiv:1008.5399 [hep-ph].3960

[115] S. Hoeche, F. Krauss, M. Schonherr, and F. Siegert,A critical appraisal of NLO+PS matching3961

methods, arXiv:1111.1220 [hep-ph]. * Temporary entry *.3962

[116] M. Cacciari, G. P. Salam, and G. Soyez,The Anti-k(t) jet clustering algorithm, JHEP0804(2008)3963

063,arXiv:0802.1189 [hep-ph].3964

[117] S. Frixione, Z. Kunszt, and A. Signer,Three jet cross-sections to next-to-leading order,3965

Nucl.Phys.B467(1996) 399–442,arXiv:hep-ph/9512328 [hep-ph].3966

[118] S. Catani and M. H. Seymour,A general algorithm for calculating jet cross sections in NLO3967

QCD, Nucl. Phys.B485(1997) 291–419,arXiv:hep-ph/9605323.3968

[119] S. Schumann and F. Krauss,A Parton shower algorithm based on Catani-Seymour dipole3969

factorisation, JHEP0803(2008) 038,arXiv:0709.1027 [hep-ph].3970

[120] Z. Nagy,Next-to-leading order calculation of three jet observables in hadron hadron collision,3971

Phys.Rev.D68 (2003) 094002,arXiv:hep-ph/0307268 [hep-ph].3972

November 18, 2011 – 11 : 26 DRAFT 199

[121] K. Hamilton and P. Nason,Improving NLO-parton shower matched simulations with higher3973

order matrix elements, JHEP1006(2010) 039,arXiv:1004.1764 [hep-ph].3974

[122] S. Hoche, F. Krauss, M. Schonherr, and F. Siegert,NLO matrix elements and truncated showers,3975

JHEP1108(2011) 123,arXiv:1009.1127 [hep-ph].3976

[123] S. Alekhin, S. Alioli, R. D. Ball, V. Bertone, J. Blumlein, et al.,The PDF4LHC Working Group3977

Interim Report, arXiv:1101.0536 [hep-ph]. * Temporary entry *.3978

[124] J.-C. Winter, F. Krauss, and G. Soff,A Modified cluster hadronization model, Eur.Phys.J.C363979


[125] B. Andersson, G. Gustafson, G. Ingelman, and T. Sjostrand,Parton Fragmentation and String3981

Dynamics, Phys.Rept.97 (1983) 31–145.3982

[126] T. Sjöstrand, S. Mrenna, and P. Z. Skands,PYTHIA 6.4 physics and manual, JHEP05 (2006)3983

026,arXiv:hep-ph/0603175.3984

[127] T. Sjostrand and M. van Zijl,A Multiple Interaction Model for the Event Structure in Hadron3985

Collisions, Phys.Rev.D36 (1987) 2019.3986

[128] C. Anastasiou, K. Melnikov, and F. Petriello,Higgs boson production at hadron colliders:3987

Differential cross sections through next-to-next-to-leading order, Phys.Rev.Lett.93 (2004)3988

262002,arXiv:hep-ph/0409088 [hep-ph].3989

[129] C. Anastasiou, K. Melnikov, and F. Petriello,Fully differential Higgs boson production and the3990

di-photon signal through next-to-next-to-leading order, Nucl. Phys.B724(2005) 197–246,3991

hep-ph/0501130.3992

[130] S. Catani and M. Grazzini,An NNLO subtraction formalism in hadron collisions and its3993

application to Higgs boson production at the LHC, Phys. Rev. Lett.98 (2007) 222002,3994

hep-ph/0703012.3995

[131] C. Balazs and C. Yuan,Higgs boson production at the LHC with soft gluon effects, Phys.Lett.3996


[132] C. Balazs, J. Huston, and I. Puljak,Higgs production: A Comparison of parton showers and3998

resummation, Phys.Rev.D63 (2001) 014021,arXiv:hep-ph/0002032 [hep-ph].3999

[133] G. Bozzi, S. Catani, D. de Florian, and M. Grazzini,Transverse-momentum resummation and the4000

spectrum of the Higgs boson at the LHC, Nucl. Phys.B737(2006) 73–120,4001


[134] C. Anastasiou, G. Dissertori, M. Grazzini, F. Stockli, and B. R. Webber,Perturbative QCD4003

effects and the search for a H-> WW-> l nu l nu signal at the Tevatron, JHEP0908(2009) 099,4004

arXiv:0905.3529 [hep-ph].4005

[135] S. Dawson,Radiative corrections to Higgs boson production, Nucl.Phys.B359(1991) 283–300.4006

[136] C. Anastasiou, S. Beerli, S. Bucherer, A. Daleo, and Z.Kunszt,Two-loop amplitudes and master4007

integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop, JHEP4008

0701(2007) 082,arXiv:hep-ph/0611236 [hep-ph].4009

[137] R. Harlander and P. Kant,Higgs production and decay: analytic results at next-to-leading order4010

QCD, JHEP0512(2005) 015,arXiv:hep-ph/0509189 [hep-ph].4011

[138] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini,Analytic results for virtual QCD corrections4012

to Higgs production and decay, JHEP01 (2007) 021,arXiv:hep-ph/0611266.4013

[139] R. Bonciani, G. Degrassi, and A. Vicini,Scalar particle contribution to Higgs production via4014

gluon fusion at NLO, JHEP11 (2007) 095,arXiv:0709.4227 [hep-ph].4015

[140] R. V. Harlander and W. B. Kilgore,Next-to-next-to-leading order Higgs production at hadron4016

colliders, Phys. Rev. Lett.88 (2002) 201801,arXiv:hep-ph/0201206.4017

[141] C. Anastasiou and K. Melnikov,Higgs boson production at hadron colliders in NNLO QCD,4018

Nucl. Phys.B646(2002) 220–256,arXiv:hep-ph/0207004.4019

November 18, 2011 – 11 : 26 DRAFT 200

[142] V. Ravindran, J. Smith, and W. L. van Neerven,NNLO corrections to the total cross section for4020

Higgs boson production in hadron hadron collisions, Nucl. Phys.B665(2003) 325–366,4021


[143] S. Marzani, R. D. Ball, V. Del Duca, S. Forte, and A. Vicini, Higgs production via gluon-gluon4023

fusion with finite top mass beyond next-to-leading order, Nucl. Phys.B800(2008) 127–145,4024

arXiv:arXiv:0801.2544 [hep-ph].4025

[144] R. V. Harlander and K. J. Ozeren,Top mass effects in Higgs production at next-to-next-to-leading4026

order QCD: virtual corrections, Phys. Lett.B679(2009) 467–472,arXiv:0907.29974027

[hep-ph].4028

[145] R. V. Harlander and K. J. Ozeren,Finite top mass effects for hadronic Higgs production at4029

next-to-next-to-leading order, JHEP11 (2009) 088,arXiv:0909.3420 [hep-ph].4030

[146] R. V. Harlander, H. Mantler, S. Marzani, and K. J. Ozeren, Higgs production in gluon fusion at4031

next-to-next-to-leading order QCD for finite top mass, Eur. Phys. J.C66 (2010) 359–372,4032

arXiv:0912.2104 [hep-ph].4033

[147] S. Catani, D. de Florian, M. Grazzini, and P. Nason,Soft-gluon resummation for Higgs boson4034

production at hadron colliders, JHEP07 (2003) 028,hep-ph/0306211.4035

[148] S. Moch and A. Vogt,Higher-order soft corrections to lepton pair and Higgs boson production,4036

Phys. Lett.B631(2005) 48–57,hep-ph/0508265.4037

[149] S. Actis, G. Passarino, C. Sturm, and S. Uccirati,Two-loop threshold singularities, unstable4038

particles and complex masses, Phys. Lett.B669(2008) 62–68,arXiv:0809.1302 [hep-ph].4039

[150] R. Bonciani, G. Degrassi, and A. Vicini,On the Generalized Harmonic Polylogarithms of One4040

Complex Variable, Comput.Phys.Commun.182(2011) 1253–1264,arXiv:1007.18914041

[hep-ph].4042

[151] C. Anastasiou, R. Boughezal, and F. Petriello,Mixed QCD-electroweak corrections to Higgs4043

boson production in gluon fusion, JHEP04 (2009) 003,arXiv:0811.3458 [hep-ph].4044

[152] C. J. Glosser and C. R. Schmidt,Next-to-leading corrections to the Higgs boson transverse4045

momentum spectrum in gluon fusion, JHEP12 (2002) 016,hep-ph/0209248.4046

[153] V. Ravindran, J. Smith, and W. L. Van Neerven,Next-to-leading order QCD corrections to4047

differential distributions of Higgs boson production in hadron hadron collisions, Nucl. Phys.4048

B634(2002) 247–290,hep-ph/0201114.4049

[154] W.-Y. Keung and F. J. Petriello,Electroweak and finite quark-mass effects on the Higgs boson4050

transverse momentum distribution, Phys. Rev.D80 (2009) 013007,arXiv:0905.27754051

[hep-ph].4052

[155] O. Brein,Electroweak and bottom quark contributions to Higgs boson plus jet production, Phys.4053

Rev.D81 (2010) 093006,arXiv:1003.4438 [hep-ph].4054

[156] C. Anastasiou, S. Bucherer, and Z. Kunszt,HPro: A NLO Monte Carlo for Higgs production via4055

gluon fusion with finite heavy quark masses, JHEP10 (2009) 068,arXiv:0907.23624056

[hep-ph].4057

[157] D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini, Transverse-momentum resummation:4058

Higgs boson production at the Tevatron and the LHC, arXiv:1109.2109 [hep-ph].4059

[158] J. Alwall, Q. Li, and F. Maltoni,Matched predictions for Higgs production via heavy-quark loops4060

in the SM and beyond, arXiv:1110.1728 [hep-ph]. * Temporary entry *.4061

[159] S. Alioli, P. Nason, C. Oleari, and E. Re,A general framework for implementing NLO4062

calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP1006(2010) 043,4063

arXiv:1002.2581 [hep-ph].4064

[160] I. W. Stewart and F. J. Tackmann,Theory Uncertainties for Higgs and Other Searches Using Jet4065

Bins, arXiv:1107.2117 [hep-ph]. * Temporary entry *.4066

November 18, 2011 – 11 : 26 DRAFT 201

[161] J. M. Campbell, R. Ellis, and C. Williams,Hadronic production of a Higgs boson and two jets at4067

next-to-leading order, Phys. Rev.D81 (2010) 074023,arXiv:1001.4495 [hep-ph].4068

[162] S. Catani, L. Cieri, G. Ferrera, D. de Florian, and M. Grazzini,Vector boson production at4069

hadron colliders: A Fully exclusive QCD calculation at NNLO, Phys.Rev.Lett.103(2009)4070

082001,arXiv:0903.2120 [hep-ph].4071

[163] J. Campbell and K. Ellis,MCFM-Monte Carlo for FeMtobarn processes, .4072

[164] C. F. Berger, C. Marcantonini, I. W. Stewart, F. J. Tackmann, and W. J. Waalewijn,Higgs4073

Production with a Central Jet Veto at NNLL+NNLO, JHEP1104(2011) 092,arXiv:1012.44804074

[hep-ph].4075

[165] U. Baur and E. W. N. Glover,Higgs Boson Production at Large Transverse Momentum in4076

Hadronic Collisions, Nucl. Phys.B339(1990) 38–66.4077

[166] D. de Florian, M. Grazzini, and Z. Kunszt,Higgs production with large transverse momentum in4078

hadronic collisions at next-to-leading order, Phys.Rev.Lett.82 (1999) 5209–5212,4079


[167] Y. L. Dokshitzer, D. Diakonov, and S. Troian,On the Transverse Momentum Distribution of4081

Massive Lepton Pairs, Phys.Lett.B79 (1978) 269–272.4082

[168] Y. L. Dokshitzer, D. Diakonov, and S. Troian,Hard Processes in Quantum Chromodynamics,4083

Phys.Rept.58 (1980) 269–395.4084

[169] G. Parisi and R. Petronzio,Small Transverse Momentum Distributions in Hard Processes,4085

Nucl.Phys.B154(1979) 427.4086

[170] G. Curci, M. Greco, and Y. Srivastava,QCD JETS FROM COHERENT STATES, Nucl.Phys.4087

B159(1979) 451.4088

[171] J. C. Collins and D. E. Soper,Back-To-Back Jets in QCD, Nucl.Phys.B193(1981) 381.4089

[172] J. C. Collins and D. E. Soper,Back-To-Back Jets: Fourier Transform from B to K-Transverse,4090

Nucl.Phys.B197(1982) 446.4091

[173] J. C. Collins, D. E. Soper, and G. F. Sterman,Transverse Momentum Distribution in Drell-Yan4092

Pair and W and Z Boson Production, Nucl.Phys.B250(1985) 199.4093

[174] J. Kodaira and L. Trentadue,Summing Soft Emission in QCD, Phys.Lett.B112(1982) 66.4094

[175] S. Catani, E. D’Emilio, and L. Trentadue,THE GLUON FORM-FACTOR TO HIGHER4095

ORDERS: GLUON GLUON ANNIHILATION AT SMALL Q-TRANSVERSE, Phys.Lett.B2114096

(1988) 335–342.4097

[176] S. Catani, D. de Florian, and M. Grazzini,Universality of nonleading logarithmic contributions4098

in transverse momentum distributions, Nucl.Phys.B596(2001) 299–312,4099


[177] S. Catani and M. Grazzini,QCD transverse-momentum resummation in gluon fusion processes,4101

Nucl.Phys.B845(2011) 297–323,arXiv:1011.3918 [hep-ph].4102

[178] D. de Florian and M. Grazzini,Next-to-next-to-leading logarithmic corrections at small4103

transverse momentum in hadronic collisions, Phys.Rev.Lett.85 (2000) 4678–4681,4104


[179] S. Catani and M. Grazzini,Higgs boson production at hadron colliders: hard-collinear4106

coefficients at the NNLO, arXiv:1106.4652 [hep-ph]. * Temporary entry *.4107

[180] T. Becher and M. Neubert,Drell-Yan production at small qT, transverse parton distributions and4108

the collinear anomaly, Eur.Phys.J.C71 (2011) 1665,arXiv:1007.4005 [hep-ph].4109

[181] R. Kauffman,Higher order corrections to Higgs boson p(T), Phys.Rev.D45 (1992) 1512–1517.4110

[182] G. Bozzi, S. Catani, D. de Florian, and M. Grazzini,The q(T) spectrum of the Higgs boson at the4111

LHC in QCD perturbation theory, Phys.Lett.B564(2003) 65–72,arXiv:hep-ph/03021044112

[hep-ph].4113

November 18, 2011 – 11 : 26 DRAFT 202

[183] E. Laenen, G. F. Sterman, and W. Vogelsang,Higher order QCD corrections in prompt photon4114

production, Phys.Rev.Lett.84 (2000) 4296–4299,arXiv:hep-ph/0002078 [hep-ph].4115

[184] A. Kulesza, G. F. Sterman, and W. Vogelsang,Joint resummation in electroweak boson4116

production, Phys.Rev.D66 (2002) 014011,arXiv:hep-ph/0202251 [hep-ph].4117

[185] S. Moch, J. A. M. Vermaseren, and A. Vogt,The three-loop splitting functions in QCD: the4118

non-singlet case, Nucl. Phys.B688(2004) 101–134,arXiv:hep-ph/0403192.4119

[186] A. Kulesza and W. J. Stirling,Nonperturbative effects and the resummed Higgs transverse4120

momentum distribution at the LHC, JHEP0312(2003) 056,arXiv:hep-ph/03072084121

[hep-ph].4122

[187] G. Watt,Parton distribution function dependence of benchmark Standard Model total cross4123

sections at the 7 TeV LHC, JHEP1109(2011) 069,arXiv:1106.5788 [hep-ph].4124

[188] I. W. Stewart, F. J. Tackmann, and W. J. Waalewijn,Factorization at the LHC: From PDFs to4125

Initial State Jets, Phys.Rev.D81 (2010) 094035,arXiv:0910.0467 [hep-ph].4126

[189] S. Asai et al.,Prospects for the search for a standard model Higgs boson in ATLAS using vector4127

boson fusion, Eur. Phys. J.C32S2(2004) 19–54,arXiv:hep-ph/0402254.4128

[190] S. Abdullin et al.,Summary of the CMS potential for the Higgs boson discovery, Eur. Phys. J.4129

C39S2(2005) 41–61.4130

[191] P. Bolzoni, F. Maltoni, S.-O. Moch, and M. Zaro,Higgs production via vector-boson fusion at4131

NNLO in QCD, Phys. Rev. Lett.105(2010) 011801,arXiv:1003.4451 [hep-ph].4132

[192] M. Ciccolini, A. Denner, and S. Dittmaier,Strong and electroweak corrections to the production4133

of Higgs + 2-jets via weak interactions at the LHC, Phys. Rev. Lett.99 (2007) 161803,4134

arXiv:0707.0381 [hep-ph].4135

[193] M. Ciccolini, A. Denner, and S. Dittmaier,Electroweak and QCD corrections to Higgs4136

production via vector-boson fusion at the LHC, Phys. Rev.D77 (2008) 013002,4137

arXiv:0710.4749 [hep-ph].4138

[194] A. Denner, S. Dittmaier, and A. Mück,HAWK: A Monte Carlo generator for the production of4139

Higgs bosons Attached to WeaK bosons at hadron colliders,4140

http://omnibus.uni-freiburg.de/~sd565/programs/hawk/hawk.html, 2010.4141

[195] K. Arnold et al.,VBFNLO: A parton level Monte Carlo for processes with electroweak bosons,4142

http://www-itp.particle.uni-karlsruhe.de/~vbfnloweb, 2009.4143

[196] T. Figy, S. Palmer, and G. Weiglein,Higgs production via weak boson fusion in the standard4144

model and the MSSM, arXiv:1012.4789 [hep-ph].4145

[197] K. Arnold, J. Bellm, G. Bozzi, M. Brieg, F. Campanario,et al.,VBFNLO: A parton level Monte4146

Carlo for processes with electroweak bosons – Manual for Version 2.5.0,4147

arXiv:arXiv:1107.4038 [hep-ph].4148

[198] K. Arnold et al.,VBFNLO: A parton level Monte Carlo for processes with electroweak bosons,4149

Comput. Phys. Commun.180(2009) 1661–1670,arXiv:0811.4559 [hep-ph].4150

[199] T. Figy and D. Zeppenfeld,QCD corrections to jet correlations in weak boson fusion, Phys. Lett.4151


[200] P. Nason and C. Oleari,NLO Higgs boson production via vector-boson fusion matchedwith4153

shower in POWHEG, JHEP02 (2010) 037,arXiv:0911.5299 [hep-ph].4154

[201] O. Brein, A. Djouadi, and R. Harlander,NNLO QCD corrections to the Higgs-strahlung4155

processes at hadron colliders, Phys. Lett.B579(2004) 149–156,arXiv:hep-ph/0307206.4156

[202] M. L. Ciccolini, S. Dittmaier, and M. Krämer,Electroweak radiative corrections to associated4157

WH andZH production at hadron colliders, Phys. Rev.D68 (2003) 073003,4158


[203] O. Brein et al.,Precision calculations for associatedWH andZH production at hadron4160

November 18, 2011 – 11 : 26 DRAFT 203

colliders, arXiv:hep-ph/0402003.4161

[204] G. Ferrera, M. Grazzini, and F. Tramontano,Associated WH production at hadron colliders: a4162

fully exclusive QCD calculation at NNLO, arXiv:1107.1164 [hep-ph]. * Temporary entry *.4163

[205] O. Brein, R. Harlander, M. Wiesemann, and T. Zirke,Top-Quark Mediated Effects in Hadronic4164

Higgs-Strahlung, arXiv:1111.0761 [hep-ph]. * Temporary entry *.4165

[206] ALEPH Collaboration,Precision Electroweak Measurements and Constraints on theStandard4166

Model, arXiv:1012.2367 [hep-ex].4167

[207] W. Beenakker et al.,Higgs radiation off top quarks at the Tevatron and the LHC, Phys. Rev. Lett.4168

87 (2001) 201805,arXiv:hep-ph/0107081.4169

[208] W. Beenakker et al.,NLO QCD corrections tott H production in hadron collisions. ((U)), Nucl.4170

Phys.B653(2003) 151–203,arXiv:hep-ph/0211352.4171

[209] L. Reina and S. Dawson,Next-to-leading order results fortt h production at the Tevatron, Phys.4172

Rev. Lett.87 (2001) 201804,arXiv:hep-ph/0107101.4173

[210] S. Dawson, L. H. Orr, L. Reina, and D. Wackeroth,Associated top quark Higgs boson production4174

at the LHC, Phys. Rev.D67 (2003) 071503,arXiv:hep-ph/0211438.4175

[211] R. Frederix et al.,Scalar and pseudoscalar Higgs production in association with a top-antitop4176

pair, Phys. Lett.B701(2011) 427–433,arXiv:1104.5613 [hep-ph].4177

[212] M. Garzelli, A. Kardos, C. Papadopoulos, and Z. Trocsanyi, Standard Model Higgs boson4178

production in association with a top anti-top pair at NLO with parton showering, Europhys.Lett.4179

96 (2011) 11001,arXiv:1108.0387 [hep-ph].4180

[213] A. Bredenstein, A. Denner, S. Dittmaier, and S. Pozzorini, NLO QCD corrections to pp→ tt bb4181

+ X at the LHC, Phys. Rev. Lett.103(2009) 012002,arXiv:0905.0110 [hep-ph].4182

[214] A. Bredenstein, A. Denner, S. Dittmaier, and S. Pozzorini, NLO QCD corrections tott bb4183

production at the LHC: 1. quark-antiquark annihilation, JHEP08 (2008) 108,4184

arXiv:0807.1248 [hep-ph].4185

[215] A. Bredenstein, A. Denner, S. Dittmaier, and S. Pozzorini, NLO QCD corrections tott bb4186

production at the LHC: 2. full hadronic results, JHEP03 (2010) 021,arXiv:1001.40064187

[hep-ph].4188

[216] G. Bevilacqua, M. Czakon, C. G. Papadopoulos, R. Pittau, and M. Worek,Assault on the NLO4189

wishlist: pp→ tt bb, JHEP09 (2009) 109,arXiv:0907.4723 [hep-ph].4190

[217] SM and NLO Multileg Working Group Collaboration, J. R.Andersen et al.,The SM and NLO4191

multileg working group: Summary report, arXiv:1003.1241 [hep-ph].4192

[218] J. Pumplin et al.,New generation of parton distributions with uncertaintiesfrom global QCD4193

analysis, JHEP07 (2002) 012,arXiv:hep-ph/0201195.4194

[219] V. Hirschi et al.,Automation of one-loop QCD corrections, JHEP05 (2011) 044,4195

arXiv:1103.0621 [hep-ph].4196

[220] G. Bevilacqua et al.,HELAC-NLO, arXiv:1110.1499 [hep-ph].4197

[221] ATLAS Collaboration Collaboration, G. Aad et al.,Search for the Standard Model Higgs boson4198

in the decay channelH → ZZ → 4l with the ATLAS detector, arXiv:1109.5945 [hep-ex]. *4199

Temporary entry *.4200

[222] Search for a Standard Model Higgs boson produced in the decaychannel H to ZZ to 4l, .4201

[223] A. Collaboration,Search for a Standard Model Higgs boson in theH → ZZ → llνν decay4202

channel with the ATLAS detector, arXiv:1109.3357 [hep-ex]. * Temporary entry *.4203

[224] H to ZZ to 2l2nu, .4204

[225] ATLAS Collaboration Collaboration, G. Aad et al.,Search for a heavy Standard Model Higgs4205

boson in the channelH → ZZ → llqq using the ATLAS detector, arXiv:1108.50644206

[hep-ex]. * Temporary entry *.4207

November 18, 2011 – 11 : 26 DRAFT 204

[226] Search for the standard model Higgs Boson in the decay channel H to ZZ to llqq at CMS, .4208

[227] Study of the Higgs to ZZ to 2l + 2τ final state with CMS detector., .4209

[228] T. Sjöstrand, S. Ask, R. Corke, S. Mrenna, and P. Skands, PYTHIA,4210

http://home.thep.lu.se/~torbjorn/Pythia.html, 2010.4211

[229] D. de Florian and M. Grazzini,Higgs production through gluon fusion: updated cross sections at4212

the Tevatron and the LHC, Phys. Lett.B674(2009) 291–294,arXiv:0901.2427 [hep-ph].4213

[230] Y. Gao et al.,Spin determination of single-produced resonances at hadron colliders, Phys. Rev.4214

D81 (2010) 075022,arXiv:1001.3396 [hep-ph].4215

[231] T. Melia, P. Nason, R. Rontsch, and G. Zanderighi,W+W-, WZ and ZZ production in the4216

POWHEG BOX, arXiv:1107.5051 [hep-ph].4217

[232] M. Grazzini,HNNLO: A MC program for Higgs boson production at hadron colliders,4218

arXiv:0806.3336 [hep-ph].4219

[233] J. M. Campbell and R. K. Ellis,An update on vector boson pair production at hadron colliders,4220

Phys. Rev.D60 (1999) 113006,arXiv:hep-ph/9905386 [hep-ph].4221

[234] J. M. Campbell, R. K. Ellis, and C. Williams,Vector boson pair production at the LHC, JHEP4222

1107(2011) 018,arXiv:1105.0020 [hep-ph].4223

[235] T. Binoth, N. Kauer, and P. Mertsch,Gluon-induced QCD corrections topp→ ZZ → ℓℓℓ′ℓ′,4224

Proc. of XVI Int. Workshop on Deep-Inelastic Scattering andRelated Topics, London, England,4225

April 2008,arXiv:0807.0024 [hep-ph].4226

[236] C. Zecher, T. Matsuura, and J. van der Bij,Leptonic signals from off-shell Z boson pairs at4227

hadron colliders, Z. Phys.C64 (1994) 219–226,arXiv:hep-ph/9404295 [hep-ph].4228

[237] T. Binoth, M. Ciccolini, N. Kauer, and M. Kramer,Gluon-inducedWW background to Higgs4229

boson searches at the LHC, JHEP0503(2005) 065,arXiv:hep-ph/0503094 [hep-ph].4230

[238] T. Binoth, M. Ciccolini, N. Kauer, and M. Kramer,Gluon-inducedW -boson pair production at4231

the LHC, JHEP0612(2006) 046,arXiv:hep-ph/0611170 [hep-ph].4232

[239] L. J. Hall, R. Rattazzi, and U. Sarid,The Top quark mass in supersymmetric SO(10) unification,4233

Phys. Rev.D50 (1994) 7048–7065,arXiv:hep-ph/9306309.4234

[240] R. Hempfling,Yukawa coupling unification with supersymmetric thresholdcorrections, Phys.4235

Rev.D49 (1994) 6168–6172.4236

[241] M. S. Carena, M. Olechowski, S. Pokorski, and C. E. M. Wagner,Electroweak symmetry4237

breaking and bottom-top Yukawa unification, Nucl. Phys.B426(1994) 269–300,4238


[242] D. M. Pierce, J. A. Bagger, K. T. Matchev, and R.-j. Zhang, Precision corrections in the minimal4240

supersymmetric standard model, Nucl. Phys.B491(1997) 3–67,arXiv:hep-ph/9606211.4241

[243] M. S. Carena, D. Garcia, U. Nierste, and C. E. M. Wagner,Effective Lagrangian for thetbH+4242

interaction in the MSSM and charged Higgs phenomenology, Nucl. Phys.B577(2000) 88–120,4243


[244] LEP Working Group for Higgs boson searches Collaboration, R. Barate et al.,Search for the4245

standard model Higgs boson at LEP, Phys. Lett.B565(2003) 61–75,arXiv:hep-ex/0306033.4246

[245] ALEPH Collaboration, S. Schael et al.,Search for neutral MSSM Higgs bosons at LEP, Eur.4247

Phys. J.C47 (2006) 547–587,arXiv:hep-ex/0602042.4248

[246] D. Graudenz, M. Spira, and P. Zerwas,QCD corrections to Higgs boson production at proton4249

proton colliders, Phys. Rev. Lett.70 (1993) 1372–1375.4250

[247] M. Spira, A. Djouadi, D. Graudenz, and P. Zerwas,SUSY Higgs production at proton colliders,4251

Phys. Lett.B318(1993) 347–353.4252

[248] R. Harlander,Supersymmetric Higgs production at the Large Hadron Collider, Eur.Phys.J.C334253

(2004) S454–S456,arXiv:hep-ph/0311005 [hep-ph].4254

November 18, 2011 – 11 : 26 DRAFT 205

[249] A. Pak, M. Rogal, and M. Steinhauser,Finite top quark mass effects in NNLO Higgs boson4255

production at LHC, JHEP02 (2010) 025,arXiv:0911.4662 [hep-ph].4256

[250] A. Pak, M. Rogal, and M. Steinhauser,Production of scalar and pseudo-scalar Higgs bosons to4257

next-to-next-to-leading order at hadron colliders, JHEP1109(2011) 088,arXiv:1107.33914258

[hep-ph]. * Temporary entry *.4259

[251] M. Mühlleitner and M. Spira,Higgs boson production via gluon fusion: squark loops at NLO4260

QCD, Nucl. Phys.B790(2008) 1–27,arXiv:hep-ph/0612254 [hep-ph].4261

[252] R. V. Harlander and M. Steinhauser,Supersymmetric Higgs production in gluon fusion at4262

next-to-leading order, JHEP0409(2004) 066,arXiv:hep-ph/0409010 [hep-ph].4263

[253] R. V. Harlander and M. Steinhauser,Hadronic Higgs production and decay in supersymmetry at4264

next-to-leading order, Phys. Lett.B574(2003) 258–268,arXiv:hep-ph/0307346 [hep-ph].4265

[254] G. Degrassi and P. Slavich,On the NLO QCD corrections to Higgs production and decay in the4266

MSSM, Nucl. Phys.B805(2008) 267–286,arXiv:0806.1495 [hep-ph].4267

[255] C. Anastasiou, S. Beerli, and A. Daleo,The two-loop QCD amplitude gg→ h,H in the minimal4268

supersymmetric standard model, Phys. Rev. Lett.100(2008) 241806,arXiv:0803.30654269

[hep-ph].4270

[256] G. Degrassi and P. Slavich,NLO QCD bottom corrections to Higgs boson production in the4271

MSSM, arXiv:1007.3465 [hep-ph].4272

[257] R. V. Harlander, F. Hofmann, and H. Mantler,Supersymmetric Higgs production in gluon fusion,4273

JHEP1102(2011) 055,arXiv:1012.3361 [hep-ph].4274

[258] D. L. Rainwater, M. Spira, and D. Zeppenfeld,Higgs boson production at hadron colliders:4275

Signal and background processes, arXiv:hep-ph/0203187 [hep-ph].4276

[259] T. Plehn,Charged Higgs boson production in bottom gluon fusion, Phys. Rev.D67 (2003)4277

014018,arXiv:hep-ph/0206121.4278

[260] F. Maltoni, Z. Sullivan, and S. Willenbrock,Higgs-boson production via bottom-quark fusion,4279


[261] S. Dittmaier, M. Krämer, and M. Spira,Higgs radiation off bottom quarks at the Tevatron and the4281

LHC, Phys. Rev.D70 (2004) 074010,arXiv:hep-ph/0309204.4282

[262] S. Dawson, C. Jackson, L. Reina, and D. Wackeroth,Exclusive Higgs boson production with4283

bottom quarks at hadron colliders, Phys. Rev.D69 (2004) 074027,arXiv:hep-ph/03110674284

[hep-ph].4285

[263] R. V. Harlander and W. B. Kilgore,Higgs boson production in bottom quark fusion at4286

next-to-next-to leading order, Phys. Rev.D68 (2003) 013001,arXiv:hep-ph/03040354287

[hep-ph].4288

[264] S. Dittmaier, M. Krämer, A. Muck, and T. Schluter,MSSM Higgs-boson production in4289

bottom-quark fusion: electroweak radiative corrections, JHEP03 (2007) 114,4290


[265] R. Harlander, M. Krämer, and M. Schumacher,Bottom-quark associated Higgs-boson4292

production: reconciling the four- and five-flavour scheme approach, CERN-PH-TH/2011-134,4293

2011 .4294

[266] S. Dawson, C. Jackson, and P. Jaiswal,SUSY QCD Corrections to Higgs-b Production : Is the4295

∆b Approximation Accurate?, Phys.Rev.D83 (2011) 115007,arXiv:1104.1631 [hep-ph].4296

[267] K. Hamilton, P. Richardson, and J. Tully,A positive-weight next-to-leading order Monte Carlo4297

simulation for Higgs boson production, JHEP04 (2009) 116,arXiv:0903.4345 [hep-ph].4298

[268] B. Allanach,SOFTSUSY: a program for calculating supersymmetric spectra,4299

Comput.Phys.Commun.143(2002) 305–331,arXiv:hep-ph/0104145 [hep-ph].4300

[269] O. Brein and W. Hollik,MSSM Higgs bosons associated with high p(T) jets at hadron colliders,4301

November 18, 2011 – 11 : 26 DRAFT 206


[270] O. Brein and W. Hollik,Distributions for MSSM Higgs boson + jet production at hadron4303

colliders, Phys.Rev.D76 (2007) 035002,arXiv:0705.2744 [hep-ph].4304

[271] CMS Collaboration Collaboration, S. Chatrchyan et al., Search for Neutral MSSM Higgs Bosons4305

Decaying to Tau Pairs inpp Collisions at√s = 7 TeV, Phys. Rev. Lett.106(2011) 231801,4306

arXiv:1104.1619 [hep-ex].4307

[272] ATLAS Collaboration, G. Aad et al.,Search for neutral MSSM Higgs bosons decaying toτ+τ−4308

pairs in proton-proton collisions at√s = 7 TeV with the ATLAS detector, Phys. Lett.B7054309

(2011) 174–192,arXiv:1107.5003 [hep-ex].4310

[273] M. S. Carena, S. Heinemeyer, C. E. M. Wagner, and G. Weiglein, Suggestions for improved4311

benchmark scenarios for Higgs- boson searches at LEP2, arXiv:hep-ph/9912223.4312

[274] U. Langenegger, M. Spira, A. Starodumov, and P. Trueb,SM and MSSM Higgs Boson4313

Production: Spectra at large transverse Momentum, JHEP0606(2006) 035,4314


[275] J. Baglio and A. Djouadi,Higgs production at the LHC, arXiv:1012.0530 [hep-ph].4316

[276] T. Figy, C. Oleari, and D. Zeppenfeld,Next-to-leading order jet distributions for Higgs boson4317

production via weak-boson fusion, Phys. Rev.D68 (2003) 073005,arXiv:hep-ph/0306109.4318

[277] T. Hahn and M. Perez-Victoria,Automatized one-loop calculations in four and D dimensions,4319

Comput. Phys. Commun.118(1999) 153–165,arXiv:hep-ph/9807565.4320

[278] G. van Oldenborgh and J. Vermaseren,New Algorithms for One Loop Integrals, Z.Phys.C464321

(1990) 425–438.4322

[279] J. Kublbeck, H. Eck, and R. Mertig,Computeralgebraic generation and calculation of Feynman4323

graphs using FeynArts and FeynCalc, Nucl.Phys.Proc.Suppl.29A (1992) 204–208.4324

[280] J. Kublbeck, M. Bohm, and A. Denner,Feyn Arts: Computer algebraic generation of Feynman4325

graphs and amplitudes, Comput. Phys. Commun.60 (1990) 165–180.4326

[281] A. Denner, H. Eck, O. Hahn, and J. Kublbeck,Feynman rules for fermion number violating4327

interactions, Nucl.Phys.B387(1992) 467–484.4328

[282] T. Hahn,Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys.4329

Commun.140(2001) 418–431,arXiv:hep-ph/0012260.4330

[283] T. Hahn and C. Schappacher,The Implementation of the minimal supersymmetric standardmodel4331

in FeynArts and FormCalc, Comput.Phys.Commun.143(2002) 54–68,arXiv:hep-ph/01053494332

[hep-ph].4333

[284] T. Hahn,A Mathematica interface for FormCalc-generated code, Comput.Phys.Commun.1784334


[285] T. Hahn and M. Rauch,News from FormCalc and LoopTools, Nucl.Phys.Proc.Suppl.157(2006)4336


[286] W. Hollik, T. Plehn, M. Rauch, and H. Rzehak,Supersymmetric Higgs bosons in weak boson4338

fusion, Phys. Rev. Lett.102(2009) 091802,arXiv:0804.2676 [hep-ph].4339

[287] M. Rauch, W. Hollik, T. Plehn, and H. Rzehak,Supersymmetric Higgs Production in4340

Vector-Boson Fusion, PoSRADCOR2009(2010) 044,arXiv:arXiv:1004.2169 [hep-ph].4341

[288] R. V. Harlander, K. J. Ozeren, and M. Wiesemann,Higgs plus jet production in bottom quark4342

annihilation at next-to-leading order, Phys.Lett.B693(2010) 269–273,arXiv:1007.54114343

[hep-ph].4344

[289] S. Catani, D. de Florian, and M. Grazzini,Direct Higgs production and jet veto at the Tevatron4345

and the LHC in NNLO QCD, JHEP0201(2002) 015,arXiv:hep-ph/0111164 [hep-ph].4346

[290] R. Harlander and M. Wiesemann,Jet-veto in bottom-quark induced Higgs production at4347

next-to-next-to-leading order, arXiv:1111.2182 [hep-ph]. * Temporary entry *.4348

November 18, 2011 – 11 : 26 DRAFT 207

[291] J. M. Campbell, R. Ellis, F. Maltoni, and S. Willenbrock, Higgs-Boson production in association4349

with a single bottom quark, Phys. Rev.D67 (2003) 095002,arXiv:hep-ph/02040934350

[hep-ph].4351

[292] A. Djouadi,The anatomy of electro-weak symmetry breaking. II: the Higgs bosons in the minimal4352

supersymmetric model, Phys. Rep.459(2008) 1–241,arXiv:hep-ph/0503173.4353

[293] CMS Collaboration,Search for Neutral Higgs Bosons Decaying to Tau Pairs in pp Collisions at4354 √s = 7 TeV, CMS PAS HIG-11-020 (2011) .4355

[294] R. Kinnunen, S. Lehti, F. Moortgat, A. Nikitenko, and M. Spira,Measurement of the H/A –> tau4356

tau cross section and possible constraints on tan beta, Eur. Phys. J.C40N5(2005) 23–32,4357


[295] ALEPH Collaboration, A. Heister et al.,Search for charged Higgs bosons ine+e− collisions at4359

energies up to√s = 209-GeV, Phys. Lett.B543(2002) 1–13,arXiv:hep-ex/0207054.4360

[296] J. F. Gunion and A. Turski,Renormalization of Higgs boson mass sum rules and screening, Phys.4361

Rev.D39 (1989) 2701.4362

[297] A. Brignole,Radiative corrections to the supersymmetric charged Higgsboson mass, Phys. Lett.4363

B277(1992) 313–323.4364

[298] M. A. Diaz and H. E. Haber,One loop radiative corrections to the charged Higgs mass of the4365

minimal supersymmetric model, Phys. Rev.D45 (1992) 4246–4260.4366

[299] CDF Collaboration, T. Aaltonen et al.,Search for charged Higgs bosons in decays of top quarks4367

in p− p collisions at√s = 1.96 TeV, Phys. Rev. Lett.103(2009) 101803,arXiv:0907.12694368

[hep-ex].4369

[300] D0 Collaboration, V. M. Abazov et al.,Search for charged Higgs bosons in top quark decays,4370

Phys. Lett.B682(2009) 278–286,arXiv:0908.1811 [hep-ex].4371

[301] S. Dittmaier, G. Hiller, T. Plehn, and M. Spannowsky,Charged-Higgs collider signals with or4372

without flavor, Phys. Rev.D77 (2008) 115001,arXiv:0708.0940 [hep-ph].4373

[302] D. Eriksson, S. Hesselbach, and J. Rathsman,Associated charged Higgs andW boson4374

production in the MSSM at the CERN large hadron collider, Eur. Phys. J.C53 (2008) 267–280,4375


[303] A. Alves and T. Plehn,Charged Higgs boson pairs at the LHC, Phys. Rev.D71 (2005) 115014,4377


[304] O. Brein and W. Hollik,Pair production of charged MSSM Higgs bosons by gluon fusion, Eur.4379

Phys. J.C13 (2000) 175–184,arXiv:hep-ph/9908529.4380

[305] S. Moch and P. Uwer,Heavy-quark pair production at two loops in QCD, Nucl. Phys. Proc.4381

Suppl.183(2008) 75–80,arXiv:0807.2794 [hep-ph].4382

[306] U. Langenfeld, S. Moch, and P. Uwer,New results for t bar t production at hadron colliders,4383

arXiv:0907.2527 [hep-ph].4384

[307] ATLAS Collaboration, G. Aad et al.,Measurement of the top quark pair production cross section4385

in pp collisions at sqrt(s) = 7 TeV in dilepton final states with ATLAS, arXiv:1108.36994386

[hep-ex].4387

[308] M. Spira,HIGLU and HDECAY: Programs for Higgs boson production at theLHC and Higgs4388

boson decay widths, Nucl. Instrum. Meth.A389 (1997) 357–360,arXiv:hep-ph/9610350.4389

[309] M. S. Carena, S. Heinemeyer, C. E. M. Wagner, and G. Weiglein, MSSM Higgs boson searches at4390

the Tevatron and the LHC: impact of different benchmark scenarios, Eur. Phys. J.C45 (2006)4391

797–814,arXiv:hep-ph/0511023.4392

[310] J. M. Campbell, R. K. Ellis, and F. Tramontano,Single top production and decay at4393

next-to-leading order, Phys. Rev.D70 (2004) 094012,arXiv:hep-ph/0408158.4394

[311] L. Hofer, U. Nierste, and D. Scherer,Resummation of tan-beta-enhanced supersymmetric loop4395

November 18, 2011 – 11 : 26 DRAFT 208

corrections beyond the decoupling limit, JHEP10 (2009) 081,arXiv:0907.5408 [hep-ph].4396

[312] G. D. Kribs, T. Plehn, M. Spannowsky, and T. M. P. Tait,Four generations and Higgs physics,4397

Phys. Rev.D76 (2007) 075016,arXiv:0706.3718 [hep-ph].4398

[313] M. Hashimoto,Constraints on Mass Spectrum of Fourth Generation Fermionsand Higgs4399

Bosons, Phys. Rev.D81 (2010) 075023,arXiv:1001.4335 [hep-ph].4400

[314] C. Anastasiou, S. Buehler, E. Furlan, F. Herzog, and A.Lazopoulos,Higgs production4401

cross-section in a Standard Model with four generations at the LHC, arXiv:1103.36454402

[hep-ph].4403

[315] C. Anastasiou, R. Boughezal, and E. Furlan,The NNLO gluon fusion Higgs production4404

cross-section with many heavy quarks, JHEP06 (2010) 101,arXiv:1003.4677 [hep-ph].4405

[316] A. Djouadi and P. Gambino,Leading electroweak correction to Higgs boson production at proton4406

colliders, Phys. Rev. Lett.73 (1994) 2528–2531,hep-ph/9406432.4407

[317] A. Djouadi, P. Gambino, and B. A. Kniehl,Two loop electroweak heavy fermion corrections to4408

Higgs boson production and decay, Nucl. Phys.B523(1998) 17–39,arXiv:hep-ph/9712330.4409

[318] F. Fugel, B. A. Kniehl, and M. Steinhauser,Two-loop electroweak correction of O(G(F) M(t)**2)4410

to the Higgs-boson decay into photons, Nucl. Phys.B702(2004) 333–345,4411


[319] X. Ruan and Z. Zhang,Impact on the Higgs Production Cross Section and Decay Branching4413

Fractions of Heavy Quarks and Leptons in a Fourth GenerationModel, arXiv:1105.16344414

[hep-ph].4415

[320] G. Passarino, C. Sturm, and S. Uccirati,Complete Electroweak Corrections to Higgs production4416

in a Standard Model with four generations at the LHC, arXiv:1108.2025 [hep-ph].4417

[321] A. Bredenstein, A. Denner, S. Dittmaier, and M. M. Weber, Precision calculations for H→4418

WW/ZZ→ 4fermions with PROPHECY4f, arXiv:0708.4123 [hep-ph].4419

[322] M. S. Chanowitz, M. Furman, and I. Hinchliffe,Weak Interactions of Ultraheavy Fermions,4420

Phys.Lett.B78 (1978) 285.4421

[323] B. A. Kniehl,Two loop O (alpha-s G(F)M(Q)2) heavy quark corrections to the interactions4422

between Higgs and intermediate bosons, Phys.Rev.D53 (1996) 6477–6485,4423


[324] G. Passarino, C. Sturm, and S. Uccirati,Higgs pseudo-observables, second Riemann sheet and4425

all that, Nucl. Phys.B834(2010) 77–115,arXiv:1001.3360 [hep-ph].4426

[325] A. Ghinculov and T. Binoth,On the position of a heavy Higgs pole, Phys.Lett.B394(1997)4427


[326] C. Anastasiou, S. Buhler, F. Herzog, and A. Lazopoulos, Total cross-section for Higgs boson4429

hadroproduction with anomalous Standard Model interactions, arXiv:1107.0683 [hep-ph].4430

[327] M. J. G. Veltman,Unitarity and causality in a renormalizable field theory with unstable4431

particles, Physica29 (1963) 186–207.4432

[328] R. Jacob and R. Sachs,Mass and Lifetime of Unstable Particles, Phys.Rev.121(1961) 350–356.4433

[329] G. Valent,Renormalization and second sheet poles in unstable particle theory, Nucl.Phys.B654434

(1973) 445–459.4435

[330] J. Lukierski,FIELD OPERATOR FOR UNSTABLE PARTICLE AND COMPLEX MASS4436

DESCRIPTION IN LOCAL QFT, Fortsch.Phys.28 (1980) 259.4437

[331] C. Bollini and L. Oxman,Unitarity and complex mass fields, Int.J.Mod.Phys.A8 (1993)4438

3185–3198.4439

[332] P. A. Grassi, B. A. Kniehl, and A. Sirlin,Width and partial widths of unstable particles in the4440

light of the Nielsen identities, Phys.Rev.D65 (2002) 085001,arXiv:hep-ph/01092284441

[hep-ph].4442

November 18, 2011 – 11 : 26 DRAFT 209

[333] P. A. Grassi, B. A. Kniehl, and A. Sirlin,Width and partial widths of unstable particles, Phys.4443

Rev. Lett.86 (2001) 389–392,arXiv:hep-th/0005149.4444

[334] B. A. Kniehl and A. Sirlin,Mass and width of a heavy Higgs boson, Phys.Lett.B440(1998)4445


[335] B. A. Kniehl and A. Sirlin,Differences between the pole and on-shell masses and widthsof the4447

Higgs boson, Phys.Rev.Lett.81 (1998) 1373–1376,arXiv:hep-ph/9805390 [hep-ph].4448

[336] A. Denner, S. Dittmaier, M. Roth, and L. Wieders,Electroweak corrections to charged-current4449

e+e− → 4 fermion processes: Technical details and further results, Nucl. Phys.B724(2005)4450


[337] S. Actis and G. Passarino,Two-loop renormalization in the standard model. III: Renormalization4452

equations and their solutions, Nucl. Phys.B777(2007) 100–156,arXiv:hep-ph/0612124.4453

[338] S. Actis and G. Passarino,Two-Loop Renormalization in the Standard Model Part II:4454

Renormalization Procedures and Computational Techniques, Nucl.Phys.B777(2007) 35–99,4455


[339] M. Cacciari and N. Houdeau,Meaningful characterisation of perturbative theoretical4457

uncertainties, JHEP1109(2011) 039,arXiv:1105.5152 [hep-ph].4458

[340] M. Krämer, E. Laenen, and M. Spira,Soft gluon radiation in Higgs boson production at the4459

LHC, Nucl. Phys.B511(1998) 523–549,arXiv:hep-ph/9611272 [hep-ph].4460

[341] R. V. Harlander and W. B. Kilgore,Soft and virtual corrections to pp→ H+X at NNLO, Phys.4461

Rev.D64 (2001) 013015,arXiv:hep-ph/0102241.4462

November 18, 2011 – 11 : 26 DRAFT 210

Appendices4463

organisation europÉenne pour la recherche ......34 report handbook of lhc higgs cross sections: 1....

Documents