Phenomenology tools for the LHC James Stirling

Cambridge University

• introduction and overview• HO corrections• PDFs LHC benchmarks• MC tools• more speculative pQCD applications• summary

apologies for omitting many topics of interest!

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1introduction and overview

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phenomenology at hadron colliders• Our goal is to make accurate predictions for

― event rates (cross sections and distributions)

― event shapes (content and structure)• QCD is at the heart of everything –

electroweak effects are generally under control • In many cases, perturbative QCD can be

used to achieve high precision• But in other contexts our understanding of the

non-perturbative QCD effects is still quite primitive, and we have to resort to models

phenomenology tools

perturbation theory: LO, NLO, NNLO, … supplemented by resummed NnLL improvements, EW corrections, …

parton distribution functions

event simulation (parton showers + tuned UE) MCs, interfaced with LO or NLO hard scattering MEs

all underpinned by the QCD factorization theorem for hard-scattering (short-distance) inclusive processes

jet algorithms

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2higher-order perturbative QCD corrections

general structure of a QCD perturbation series

• choose a renormalisation scheme (e.g. MSbar)• calculate cross section to some order (e.g. NLO)

• note d/d=0 “to all orders”, but in practice d(N+n)/d= O((N+n)S

N+n+1) as many orders as possible!

• can try to help convergence by using a “physical scale choice”, ~ P , e.g. = MZ or = ET

jet

• what if there is a wide range of P’s in the process, e.g. W + n jets? – see later

physical variable(s)

process dependent coefficientsdepending on P

renormalisationscale

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how precise?• LO for generic PS Monte Carlos, tree-

level MEs

• NLO for NLO-MCs and many parton-level signal and background processes – in principle, less sensitivity to

unphysical renormalisation and factorisation scales, μR and μF– parton merging to give structure in jets

– more types of incoming partons – more reliable pdfs– better description of final state

kinematics

• NNLO for a limited number of ‘precision observables’ (W, Z, DY, H, …)

+ E/W corrections, resummed HO terms etc…

?

NNLO

NLO

NNLO

NLO

NLO

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recent developments at NLO• traditional methods based on Feynman diagrams, then reduction to

known (scalar box, triangle, bubble and tadpole) integrals

• … and new methods based on unitarity and on-shell recursion: assemble loop-diagrams from individual tree-level diagrams– basic idea: Bern, Dixon, Kosower 1993– cuts with respect to on-shell complex loop momenta:

Cachazo, Britto, Feng 2004– tensor reduction scheme: Ossola, Pittau, Papadopoulos 2006– integrating the OPP procedure with unitarity: Ellis, Giele, Kunszt 2008– D-dimensional unitarity: Giele, Kunszt, Melnikov 2008– …

• … and the appearance of automated programmes for one-loop, multi-leg amplitudes, either based on – traditional or numerical Feynman approaches (Golem, …)– unitarity/recursion (BlackHat, CutTools, Rocket, …)

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some recent NLO results…*• pp W+3j [Rocket: Ellis, Melnikov & Zanderighi]

[unitarity]• pp W+3j [BlackHat: Berger et al]

[unitarity]• pp tt bb [Bredenstein et al] [traditional]• pp tt bb [HELAC-NLO: Bevilacqua et al] [unitarity]• pp qq 4b [Golem: Binoth et al] [traditional]• pp tt+2j [HELAC-NLO: Bevilacqua et al] [unitarity]• pp Z+3j [BlackHat: Berger et al]

[unitarity]• pp W+4j [BlackHat: Berger et al, partial]

[unitarity]• …

with earlier results on V,H + 2 jets, VV,tt + 1 jet, VVV, ttH, ttZ, …

In contrast, for NNLO we still only have inclusive *,W,Z,H with rapidity distributions and decays (although much progress on top, single jet, …)*relevant for LHC

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Top at Tevatron

Bottom at LHC

reason: new processes open up at NLO!

K. Ellis

K. Ellis

in complicated processes like W + n jets, there are often many ‘reasonable’ choices of scales:

‘blended’ scales like HT can seamlessly take account of different kinematical configurations:

Berger et al., arXiv:0907.1984

However...

the impact of NNLO: W,Z

Anastasiou, Dixon, Melnikov, Petriello, 2004

• only scale variation uncertainty shown• central values calculated for a fixed set pdfs with a fixed value of S(MZ

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Harlander,KilgoreAnastasiou, MelnikovRavindran, Smith, van Neerven …

• the NNLO band is about 10%, or 15% if R and F varied independently

the impact of NNLO: Higgs

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SM Higgs: Tevatron exclusion limits

cross sectiontheory

uncertainty

?

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3parton distribution functions

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pdfs @ LHC

*

SUSY,Higgs,W,Z,…

• most SM and new physics sample pdfs in a region of x where they are already well known

• current pdf uncertainties provide the benchmark for whether LHC can add new information

• low-mass forward production (e.g. b quarks, Drell-Yan) might provide new information on small-x partons

proton

x1P

proton

x2PX

DGLAP evolution

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the pdf industry• many groups now extracting pdfs from ‘global’

data analyses (MSTW, CTEQ, NNPDF, HERAPDF, AKBM, GJR, …)

• broad agreement, but differences due to– choice of data sets (including cuts and corrections)– treatment of data errors– treatment of heavy quarks (s,c,b)– order of perturbation theory– parameterisation at Q0

– theoretical assumptions (if any) about: • flavour symmetries• x→0,1 behaviour• …

– definition of pdf uncertainties

HERA-DISFT-DIS

Drell-YanTevatron jetsTevatron W,Z

other

pdfs authors arXiv

ABKM S. Alekhin, J. Blümlein, S. Klein, S. Moch, and others

1101.5261, 1007.3657, 0908.3128, 0908.2766, …

CTEQH.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. Nadolsky, J. Pumplin, C.-P. Yuan, and others

1007.2241, 1004.4624, 0910.4183, 0904.2424, 0802.0007, …

GJR M. Glück, P. Jimenez-Delgado, E. Reya, and others

1006.5890, 0909.1711, 0810.4274, …

HERAPDF H1 and ZEUS collaborations 1006.4471, 0906.1108, …

MSTW A.D. Martin, W.J. Stirling, R.S. Thorne, G. Watt

1006.2753, 0905.3531, 0901.0002, …

NNPDFR. Ball, L. Del Debbio, S. Forte, A. Guffanti, J. Latorre, J. Rojo, M. Ubiali, and others

1103.2369, 1101.1300, 1012.0836, 1005.0397, 1002.4407, 0912.2276, 0906.1958, …

recent global or quasi-global pdf fits

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MSTW08 CT10 NNPDF2.1 HERAPDF1.0/1.5 ABKM09 GJR08

HERA DIS F-T DIS F-T DY TEV W,Z TEV jets

GM-VFNS NNLO Note:• each set comes with its own unique S(MZ

2) value (and uncertainty), correlated with the pdfs

• CT10, HERAPDF, NNPDF2.1 use recent combined HERA data

• NNPDF2.5(NNLO) soon

21MSTW = Martin, S, Thorne, Watt

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4LHC benchmark cross sections

the following luminosity and cross section plots are from Graeme Watt: these and many more available at projects.hepforge.org/mstwpdf/pdf4lhc

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parton luminosity* comparisonsRun 1 vs. Run 2 Tevatron jet data

positivity constraint on input gluon

momentum sum ruleZM-VFNS

No Tevatron jet data or FT-DIS data in fit

*

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benchmark W,Z cross sections

G. Watt, 2011

New CMS 36pb-1 result (CMS-PAS-EWK-10-005):

R± = 1.421 ± 0.006(stat) ± 0.014(syst) ± 0.030(th)

from extrapolation to full acceptance; better to calculate and compare for experimental acceptance

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Wl rapidity asymmetry

• very sensitive to pdfs• complex interplay of uV, dV,

Sea, V ± A decay• 7 TeV data! 0 1 2 3 4 5

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

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W asymmetry lepton asymmetry,

variable pTlep

(min)

02010

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A+-(y

)

ylep

or yW

LHC 7 TeVMSTW2008 NLO

W

l±

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SM Higgs and top cross sections

G. Watt, 2011

… differences from both pdfs AND S !

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5MC Tools*

*For a recent review, see Peter Richardson, ‘Challenging the Standard Model’ IoP Half-Day meeting, indico.cern.ch/conferenceDisplay.py?ovw=True&confId=112764

Monte Carlo Event Generators• programs that simulates particle physics events with the same

probability as they occur in nature• widely used for signal and background estimates• examples are PYTHIA, HERWIG, SHERPA , ...• the simulation comprises different phases:

a) start by simulating a hard scattering process (LO, NLO)b) this is followed by the simulation of (soft and collinear) QCD radiation

using a parton shower algorithmc) non-perturbative models are then used to simulate the hadronization of the

quarks and gluons into the observed hadrons and the underlying event• a) and b) well grounded theoretically, c) requires a model to be tuned to

data:– parameters relating to the final-state parton shower and hadronization are

tuned to LEP data– parameters relating to initial-state parton showers and multiple parton-

parton interactions are tuned to data (e.g. UA5, Tevatron) – extrapolation to LHC?!

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“PYTHIA AMBT1 and HERWIG+JIMMY AUET1 tunes from ATLAS give a good description of ATLAS soft QCD physics without severely compromising Tevatron agreement.”

A. Buckley for ATLAS, Knoxville, November 2010

PYTHIA tunes to ATLAS 7 TeV MinBias data

+

interfacing NnLO and parton showers

Benefits of both:

NnLO correct overall rate, hard scattering kinematics, reduced scale dep.PS complete event picture, correct treatment of collinear logs to all orders

• MC@NLO (Frixione, Webber, et al ): large range of processes available, integrated with Herwig FORTRAN and Herwig++ programs

• POWHEG (Nason): fewer processes, either standalone (Alioli, Nason, Oleari, Re) or integrated with Herwig++ (Hamilton, Richardson, Tully) or SHERPA (Hoeche, Krauss, Schonherr, Siegert)

(hadron collider) processes in MC@NLO

from the MC@NLO 4.0 manual

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HW++ vs. POWHEG vs. MC@NLO vs. MCFM

Tevatron Z0Z0 LHC W+W-

POWHEG vs. ATLAS jet data

Herwig++ 2.5 Release Note (S. Gieseke et al) arXiv:1102.1672 [hep-ph]

S. Alioli et al, arXiv:1012.3380 [hep-ph]

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Jet algorithms• Snowmass accord (1990)

a) simple to implement in experimental analyses as well as theory calculationsb) defined at any order in pQCD and yields finite results for rates at any orderc) yields a cross-section relatively insensitive to hadronisation

• two main types– CONES: latest implementation SISCONE (Salam, Soyez, 2007)– SUCCESSIVE RECOMBINATION: Jade ... kT ... anti-kT (Cacciari, Salam,

Soyez 2008)

• anti-kT : hard stuff clusters with nearest neighbour, privilege collinear divergence over soft divergence; gives cone-like jets without using cones!

{phi} {jk} {partons}

Gavin Salam, “Towards Jetography” (2009)

Finally, a straightforward, robust, widely-accepted algorithm for jet studies at LHC that satisfies Snowmass accord ...

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6finally, there are interesting processeswhere our theoretical understanding

is much less developed...

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central exclusive production

• p + p H + X– the rate (parton, pdfs, αS)– the kinematic distribtns. (d/dydpT)– the environment (jets, underlying

event, backgrounds, …)

• p + p p + H + p– a real challenge for theory (pQCD

+ npQCD) and experiment (tagging forward protons, triggering, …)

compare …

with …

b

b

• colliding protons interact via a colour singlet exchange and remain intact: can be triggered by adding proton detectors far down the beam-pipe or by using large rapidity gaps

• a system of mass MX is produced at the collision point, and only its decay products are present in the central detector region.

• the generic process pp → p + X + p is modeled perturbatively by the exchange of two t-channel gluons (‘Durham Model’ – Khoze Martin Ryskin)

• the possibility of additional soft rescatterings filling the rapidity gaps is encoded in ‘eikonal’ and ‘enhanced’ survival factors

p + p → p X p

Xga

p su

rviv

al

central exclusive production – theory

CEP at LHC?

• in the limit that the outgoing protons scatter at zero angle, the centrally produced state X must have JZ

P = 0+ quantum numbers → spin-parity filter/analyser

• in certain regions of MSSM parameter space, couplings of Higgs to bb is enhanced, and CEP could be the discovery channel

• or any exotic 0++ state, which couples strongly to glue, is a real possibility: radions, gluinoballs, …

• in the meantime, many ‘standard candle’ processes at RHIC, Tevatron, LHC: X= jj, , c, b, …

• example:

p + p → p X p

X

CDF(arXiv:0902.1271):

KHRYSTHAL (Khoze, Ryskin, S, Harland-Lang, arXiv:1005.0695 ):

Durham/St Petersburg /Cambridge (Khoze, Martin, Ryskin, S, Harland-Lang,....)

Manchester (Cox, Forshaw, Monk, Pilkington, Coughlin, ...)

Helsinki (Orava, ...)

Saclay (Royon, ...)

Cracow (Szczurek, ...)…

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single and double hard parton scattering

• folklore

• studies of +3j production by CDF and D0 suggest eff ≈ 15 mb• use shape variables as a discriminator for DPS • however, simple factorisation hypothesis

now being called into question much recent theoretical activity, see

X,Y distinct: m=2X,Y same: m=1

DPS + SPS SPS

 MPI@LHC 2010: 2nd International Workshop on Multiple Partonic Interactions at the LHC, Glasgow, November 2010, www.mpi2010.physics.gla.ac.uk

e.g. X,Y = jj,bb,W,Z,J/,..

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summary

• relentless advance in improving phenomenology tools for precision hadron collider physics in recent years

– the NLO revolution (but still ‘scale choice/variation’ issues), with NNLO the next frontier (but no “+jet” processes yet)

– PDFs: convergence among groups and first precision tests at LHC

– Monte Carlo: improved modelling, new tunes to LHC and increasing number of NLO processes included (e.g. MC@NLO, POWHEG, ... )

• … and don’t forget other more novel applications of pQCD (hard diffraction, multiple parton interactions, etc.) where more theoretical work and experimental data are needed

extra slides

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pdfs and S(MZ2)

• MSTW08, ABKM09 and GJR08: S(MZ

2) values and uncertainty determined by global fit

• NNLO value about 0.003 0.004 lower than NLO value, e.g. for MSTW08

• CTEQ, NNPDF, HERAPDF choose standard values and uncertainties

• world average (PDG 2009)

• note that the pdfs and S are correlated!

• e.g. gluon – S anticorrelation at small x and quark – S anticorrelation at large x

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parton luminosity functions• a quick and easy way to assess the mass, collider

energy and pdf dependence of production cross sections

• i.e. all the mass and energy dependence is contained in the X-independent parton luminosity function in [ ]

• useful combinations are • and also useful for assessing the uncertainty on cross

sections due to uncertainties in the pdfs (see later)

s Xa

b

Trest 2007 47

CEP hMSSMbb at LHC

Heinemeyer, Khoze, Ryskin, S, Tasevsky, Weiglein: arXiv:0708.3052

3 statistical significance contours, Mh

max scenario