james stirling ippp, university of durham thanks to qcd-hard and qcd-soft parallel session...

James Stirling

IPPP, University of Durham

Thanks to QCD-Hard and QCD-Soft parallel session organisers and speakers!

QCD Theory

– a status report and review of some developments in the past year

QCD - ICHEP04 2J Stirling

more QCD? … see also

QCD @ HERA: Klein

QCD @ Tevatron: Lucchesi

QCD and hadron spectroscopy: Close, Shan Jin

QCD and heavy quarks: Ali, Shipsey

QCD on the Lattice: Hashimoto


QCD is …

• an essential and established* part of the toolkit for discovering physics beyond the standard model, e.g. at Tevatron and LHC

• a Yang-Mills gauge field theory with a very rich structure (asymptotic freedom confinement), much of which is not yet fully understood in a quantitative way

* we no longer “test QCD”!


QCD in 2004

compare tot(pp) and tot(e+e-hadrons)

for ‘hard’ processes (i.e. suitably inclusive, with at least one large momentum transfer scale), QCD is a precision tool – calculations and phenomenology aiming at the per-cent level

for semi-hard, exclusive and soft processes, we need to extend and test calculational techniques

experiment and theory working together

E0

1

αS(E)

non-perturbative approaches:lattice, Regge theory, skyrmions, large-Nc,…

perturbative field theory calculations

World Summary of αS(MZ) – July 2004from S. Bethke, hep-ex/0407021

world average (MSbar, NNLO)

αS(MZ) = 0.1182 0.0027

cf. (2002) 0.1183 0.0027

New at this conference:

•ZEUS DIS + jets pdf fit•HERA jet cross sections and shape variables•JADE 4-jet rate and jet shape moments•LEP 1,2 jet shape observables, 4-jet rate

All NLO and all consistent with world average


examples of ‘precision’ phenomenologyW, Z productionjet production

NNLO QCDNLO QCD

… and many other examples presented at this Conference


status of pQCD calculations

LO– automated codes for arbitrary

matrix element generation (MADGRAPH, COMPHEP, HELAC, …)

– jet = parton, but ‘easy’ to interface to hadronisation MCs

– large scale dependence αS()N therefore not good for precision analyses

NLO– now known for ‘most’ processes of

interest– dV

(N) + dR(N+1)

– reduced scale dependence (but can still dominate αS measurement)

– jet structure begins to emerge– no automation yet, but many ideas– now can interface with PS

fixed order: d = A αSN [ 1 + C1 αS

+ C2 αS2 + …. ]

thus LO, NLO, NNLO, etc, or resummed to all orders using a leading log approximation, e.g.

d = A αSN [ 1 + (c11 L + c10 ) αS

+ (c22 L2 + c21 L + c20 ) αS2 +

…. ]

where L = log(M/qT), log(1/x), log(1-T), … >> 1 thus LL, NLL, NNLL, etc.

current frontier

1

+

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

Example: MC@NLO Frixione, Webber, Nason,www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/

processes included so far … pp WW,WZ,ZZ,bb,tt,H0,W,Z/

pT distribution of tt at Tevatron

new


t

tb

b

not all NLO corrections are known!the more external coloured particles, the more difficult the NLO pQCD calculation

Example: pp →ttbb + Xbkgd. to ttH

the leading order O(αS4) cross

section has a large renormalisation scale dependence!

QCD - ICHEP04 10J Stirling John Campbell, Collider Physics Workshop, KITP, January 2004

Too many calculations,too few people!


NNLO: the perturbative frontier

The NNLO coefficient C is not yet known, the curves show guesses C=0 (solid), C=±B2/A (dashed) → the scale dependence and hence σth is significantly reduced

Other advantages of NNLO: • better matching of partons hadrons• reduced power corrections• better description of final state kinematics (e.g. transverse momentum)Glover

Tevatron jet inclusive cross section at ET = 100 GeV

Example: jet cross section at hadron colliders

2

(also e+e- 3 jets)

anatomy of a NNLO calculation: p + p jet + X

• 2 loop, 2 parton final state

• | 1 loop |2, 2 parton final state

• 1 loop, 3 parton final states or 2 +1 final state

• tree, 4 parton final states or 3 + 1 parton final states or 2 + 2 parton final state

soft, collinear

the collinear and soft singularities exactly cancel between the N +1 and N + 1-loop contributions


rapid progress in last two years [many authors]

• many 2→2 scattering processes with up to one off-shell leg now calculated at two loops

• … to be combined with the tree-level 2→4, the one-loop 2→3 and the self-interference of the one-loop 2→2 to yield physical NNLO cross sections

• the key is to identify and calculate the ‘subtraction terms’ which add and subtract to render the loop (analytically) and real emission (numerically) contributions finite

• this is still some way away but lots of ideas so expect progress soon!


summary of NNLO calculations (~1990 )

• DIS pol. and unpol. structure function coefficient functions• Sum Rules (GLS, Bj, …)• DGLAP splitting functions Moch Vermaseren Vogt (2004)

• total hadronic cross section, and Z hadrons, + hadrons• heavy quark pair production near threshold• CF

3 part of (3 jet) Gehrmann-De Ridder, Gehrmann, Glover(2004)

• inclusive W,Z,* van Neerven et al, Harlander and Kilgore corrected (2002)

• inclusive * polarised Ravindran, Smith, Van Neerven (2003)

• W,Z,* differential rapidity disn Anastasiou, Dixon, Melnikov, Petriello (2003)

• H0, A0 Harlander and Kilgore; Anastasiou and Melnikov; Ravindran, Smith, Van Neerven (2002-3)

• WH, ZH Brein, Djouadi, Harlander (2003)

• QQ onium and Qq meson decay rates+ other partial/approximate results (e.g. soft, collinear) and NNLL improvements

ep

e+e-

pp

HQ


1972-77 1977-80 2004

Note: need to know splitting and coefficient functions to the same perturbative order to ensure that (n)/logF = O(αS

(n+1))

>1991

new

The calculation of the complete set of P(2) splitting functions completes the calculational tools for a consistent NNLO pQCD treatment of Tevatron & LHC hard-scattering cross sections!


Full 3-loop (NNLO) DGLAP splitting functions!

Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111

previous estimates based on known moments and leading behaviours

Moch

a

bPba =


7 pages later…

…then 8 pages of the same quantities expressed in x-space!

Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111

σ(W) and σ(Z) : precision predictions and measurements at the Tevatron and LHC

• the pQCD series appears to be under control

• with sufficient theoretical precision, these ‘standard candle’ processes could be used to measure the machine luminosity

4% total error(MRST 2002)

NNLO phenomenology already under way…


resummation

Work continues to refine the predictions for ‘Sudakov’ processes, e.g. for the Higgs or Z transverse momentum distribution, where resummation of large logarithms of the form

n,m αSn log(M2/qT

2)m

is necessary at small qT, to be matched with fixed-order QCD at large qT

(also: event shapes, heavy quark prodn.)

Bozzi Catani de FlorianGrazzini

qT (GeV)

KuleszaStermanVogelsang

Z

De FlorianMarchesini

3


resummation contd. - HO corrections to (Higgs)

• the HO pQCD corrections to (gg→H) are large (more diagrams, more colour)

• can improve NNLO precision slightly by resumming additional soft/collinear higher-order logarithms

• example: σ(MH=120 GeV) @ LHC

σpdf ±3%

σptNNL0 ± 10%, σptNNLL ± 8%

σtheory ± 9%

Ht

g

g

Catani et al, hep-ph/0306211

H

g

gthreshold logs

logN(1-M2/sgg)


dawn of a new calculational era?

• (numerical) calculation of QCD tree-level scattering amplitudes can be automated … but method is “brute force”, and multiparton complexity soon saturates computer capability

• no automation in sight for loop amplitudes

• analytic expressions are very lengthy (recall P(2))

• a recent paper by Cachazo, Svrcek and Witten may be the long-awaited breakthrough …

Bern

4


slide from Zvi Berngg ggggg ggg


the Parke-Taylor amplitude mystery

• consider a n-gluon scattering amplitude with helicity labels

• Parke and Taylor (PRL 56 (1986) 2459):“this result is an educated guess”“we do not expect such a simple expression for the other helicity amplitudes”“we challenge the string theorists to prove more rigorously that [it] is correct”

• Witten, December 2003 (hep-th/0312171) “Perturbative gauge theory as a string theory in twistor space”

MaximumHelicityViolating

true!

rs

=

(colour factors suppressed)


Cachazo, Svrcek, Witten (CSW)

• elevate MHV scattering amplitudes to effective vertices in a new scalar graph approach

• and use them with scalar propagators to calculate

– tree-level non-MHV amplitudes

– with both quarks and gluons

– … and loop diagrams!

• dramatic simplification: compact

output in terms of familiar spinor

products

• phenomenology? multijet cross sections at LHC etc

April 2004, hep-th/0403047

Georgiou, Khoze; Zhu; Wu, Zhu; Bena, Bern, Kosower; Georgiou, Khoze, Glover; Kosower; Brandhuber, Spence, Travaglini; Bern, del Duca, Dixon, Kosower; …


the ‘other frontier’…

• 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 (rapidity gaps, forward protons, ..)

compare …

with …

b

b

The most sophisticated calculations and input from many other experiments are needed to

properly address these issues!

5

hard double pomeron

hard color singlet exchange

‘rapidity gap’ collision events

DDtypical jet event

hard single diffraction


For example: Khoze, Martin, Ryskin (hep-ph/0210094)

MH = 120 GeV, L = 30 fb-1 , Mmiss = 1 GeV

Nsig = 11, Nbkgd = 4 3σ effect ?!

Need to calculate production amplitude and gap Survival Factor: mix of pQCD and npQCD significant uncertainties

BUT calibration possible via X = quarkonia, large ET jet pair, , etc. at Tevatron

QCD challenge: to refine and test calculations & elevate to precision predictions!

selection rules

anything that

couples to gluons

GallinaroRoyon

mass resolution is crucial! Royon et al

p + p → p H p at LHC

gap

surv

ival

X

S/B

mass resolution


summaryQCD theory – major advances in the past year, with promise of more to come…

• pQCD calculations at the NNLO/NNLL frontier (e.g. jet cross sections in pp, e+e-), but many NLO “background” calculations still missing

• CSW: a new approach still in its infancy (4 months!), but with major potential

• away from “hard inclusive”, there are many calculational challenges (semi-hard, power corrections, exclusive, diffractive, …) – close collaboration with experiment is essential


extra slides


• comparison of resummed / fixed-order calculations for Higgs (MH = 125 GeV) qT distribution at LHC

Balazs et al, hep-ph/0403052

• differences due mainly to different NnLO and NnLL contributions included

• Tevatron d(Z)/dqT

provides good test of calculations

linear scalelog scale


technical details

q

g

etc.

L = log(Q2/2)

F = A L3 + B L2 + C L + D

P(2) contained in this term

number of diagrams (QGRAF)

fictitious scalar-gluon vertex

a

b


World Summary of MW

from LEPEWWG, Summer 2004

could well be a missing strong

interaction effect


the interplay of electroweak and QCD precision physics

• role of αS in global electroweak fit

• hadronic contributions to muon g-2

• use of (W) and (Z) as ‘standard candles’ to measure luminosity at LHC

• inclusion of O(α) QED effects in DGLAP evolution

• effect of hadronic structure on extraction of sin2W from N scattering

• …

2

Ward

HoeckerVainshtein


QED effects in pdfs

included in standard radiative correction packages (HECTOR, HERACLES)

• QED corrections to DIS include:

mass singularity ~α log(Q2/mq2) when ║q

• these corrections are universal and can be absorbed into pdfs, exactly as for QCD singularities, leaving finite (as mq 0) O(α) QED corrections in coefficient functions

• relevant for electroweak correction calculations for processes at Tevatron& LHC, e.g. W, Z, WH, … (see e.g. U. Baur et al, PRD 59 (2003) 013002)


QED-improved DGLAP equations• at leading order in α and αS

where

• momentum conservation:


• effect on quark distributions negligible at small x where gluon contribution dominates DGLAP evolution

• at large x, effect only becomes noticeable (order percent) at very large Q2, where it is equivalent to a shift in αS of αS 0.0003

• dynamic generation of photon parton distribution

• isospin violation: up(x) ≠ dn(x)

• first consistent global pdf fit with QED corrections included (MRST 2004)

proton

neutron

new


perturbative generation of s(x) ≠ s(x)

Pus(x) ≠ Pus(x)at O(αS

3)

Quantitative study by de Florian et alhep-ph/0404240

x(s-s)pQCD < 0.0005

cf. from global pdf fit (Olness et al, hep-ph/0312322,3)

0.001 < x(s-s)fit < +0.004

partial explanation of NuTeV sin2W “anomaly”?

note!

new


sin2W from N

3 difference

new


Conclusion: uncertainties in detailed parton structure are substantial on the scale of the precision of the NuTeV data – consistency with the Standard Model does not appear to be ruled out at present


For example: Higgs at LHC (Khoze, Martin, Ryskin hep-ph/0210094)

MH = 120 GeV, L = 30 fb-1 , Mmiss = 1 GeV

Nsig = 11, Nbkgd = 4 3σ effect ?!

need to calculate production amplitude and gap Survival Factor big uncertainties

BUT calibration possible via X = quarkonia or large ET jet pair, e.g. CDF ‘observation’ of p + p → p + χ0

c (→J/ γ) + p:

excl (J/ γ) < 49 ± 18 (stat) ± 39 (syst) pb

cf. thy ~ 70 pb (Khoze et al 2004)

QCD challenge: to refine and test such models & elevate to precision predictions!

selection rules

couples to gluons

GallinaroRoyon

mass resolution is crucial! Royon et al

new


NNLO corrections to Drell-Yan cross sections

Anastasiou et al. hep-ph/0306192hep-ph/0312266

• in DY, sizeable HO pQCD corrections since αS (M) not so small

• for σ(W), σ(Z) at Tevatron and LHC, allows QCD prediction to be matched for (finite) experimental acceptance in boson rapidity


top quark productionawaits full NNLO pQCD calculation; NNLO & NnLL “soft+virtual” approximations exist (Cacciari et al, Kidonakis et al), probably OK for

Tevatron at ~ 10% level (> σpdf )

Kidonakis and Vogt, hep-ph/0308222 LO

NNLO(S+V)

NLO

Tevatron

… but such approximations work less well at LHC energies


• Different code types, e.g.:– tree-level generic (e.g. MADEVENT)

– NLO in QCD for specific processes (e.g. MCFM)

– fixed-order/PS hybrids (e.g. MC@NLO)

– parton shower (e.g. HERWIG)

HEPCODE: a comprehensive list of publicly available cross-section codes for high-energy collider processes, with links to source or contact person

www.ippp.dur.ac.uk/HEPCODE/


pdfs from global fits

FormalismNLO DGLAPMSbar factorisationQ0

2

functional form @ Q02

sea quark (a)symmetryetc.

Who?Alekhin, CTEQ, MRST,GKK, Botje, H1, ZEUS,GRV, BFP, …

http://durpdg.dur.ac.uk/hepdata/pdf.html

DataDIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … )Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0)W rapidity asymmetry (CDF)N dimuon (CCFR, NuTeV)etc.

fi (x,Q2) fi (x,Q2)

αS(MZ )


(MRST) parton distributions in the proton

10-3

10-2

10-1

100

0.0

0.2

0.4

0.6

0.8

1.0

1.2

MRST2001

Q2 = 10 GeV

2

up down antiup antidown strange charm gluon

x

f(x,

Q2 )

x Martin, Roberts, S, Thorne


uncertainty in gluon distribution (CTEQ)

then fg → σgg→X etc.


solid = LHCdashed = Tevatron

Alekhin 2002

pdf uncertainties encoded in parton-parton luminosity functions:

with = M2/s, so that for ab→X


10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

100

101

102

103

104

105

106

107

108

109

fixedtarget

HERA

x1,2

= (M/1.96 TeV) exp(y)Q = M

Tevatron parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

422 04y =

Q2

(GeV

2 )

x10

-710

-610

-510

-410

-310

-210

-110

010

0

101

102

103

104

105

106

107

108

109

fixedtarget

HERA

x1,2

= (M/14 TeV) exp(y)Q = M

LHC parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

M = 10 TeV

66y = 40 224

Q2

(GeV

2 )

x

longer Q2

extrapolation

smaller x


Djouadi & Ferrag, hep-ph/0310209

Higgs cross section: dependence on pdfs


Djouadi & Ferrag, hep-ph/0310209


Djouadi & Ferrag, hep-ph/0310209the differences between pdf sets needs to be better understood!


why do ‘best fit’ pdfs and errors differ?

• different data sets in fit– different subselection of data

– different treatment of exp. sys. errors

• different choice of

– tolerance to define fi (CTEQ: Δχ2=100, Alekhin: Δχ2=1)

– factorisation/renormalisation scheme/scale

– Q02

– parametric form Axa(1-x)b[..] etc

– αS

– treatment of heavy flavours

– theoretical assumptions about x→0,1 behaviour

– theoretical assumptions about sea flavour symmetry

– evolution and cross section codes (removable differences!) → see ongoing HERA-LHC Workshop PDF Working Group


where X=W, Z, H, high-ET jets, SUSY sparticles, black hole, …, and Q is the ‘hard scale’ (e.g. = MX), usually F = R = Q, and is known …

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

^

… at hadron colliders

DGLAP equations


x dependence of fi(x,Q2) determined by ‘global fit’ to deep inelastic scattering (H1, ZEUS, NMC, …) and hadron collider data

F2(x,Q2) = q eq2 x q(x,Q2) etc

DGLAP equations


Scattering processes at high energy hadron colliders can be classified as either HARD or SOFT

Quantum Chromodynamics (QCD) is the underlying theory for all such processes, but the approach (and the level of understanding) is very different for the two cases

For HARD processes, e.g. W or high-ET jet production, the rates and event properties can be predicted with some precision using perturbation theory

For SOFT processes, e.g. the total cross section or diffractive processes, the rates and properties are dominated by non-perturbative QCD effects, which are much less well understood

Calculate, Predict & Test

Model, Fit, Extrapolate & Pray!


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

^

proton

jet

jet

antiproton

P x1P

x2P P

where X=W, Z, H, high-ET jets, SUSY sparticles, black hole, …, and Q is the ‘hard scale’ (e.g. = MX), usually F = R = Q, and is known …

• to some fixed order in pQCD and EWpt, e.g.

• or in some leading logarithm approximation (LL, NLL, …) to all orders via resummation


DGLAP evolution

momentum fractions x1 and x2 determined by mass and rapidity of X

x dependence of fi(x,Q2) determined by ‘global fit’ (MRST, CTEQ, …) to deep inelastic scattering (H1, ZEUS, …) data*, Q2 dependence determined by DGLAP equations:

* F2(x,Q2) = q eq2 x q(x,Q2) etc


what limits the precision of the predictions?

• the order of the perturbative expansion

• the uncertainty in the input parton distribution functions

• example: σ(Z) @ LHC

σpdf ±3%, σpt ± 2%

→ σtheory ± 4% whereas for gg→H :

σpdf << σpt

14

15

16

17

18

19

20

21

22

23

24

partons: MRST2002NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. momentsNNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections

NLONNLO

LO

LHC Z(x10)

W

. B

l (

nb)

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

NNLONLO

LO

Tevatron (Run 2)

CDF D0(e) D0()

Z(x10)

W

CDF D0(e) D0()

. B

l (

nb)



pdfs at LHC

• high precision (SM and BSM) cross section predictions require precision pdfs: th = pdf + …

• ‘standard candle’ processes (e.g. Z) to– check formalism – measure machine luminosity?

• learning more about pdfs from LHC measurements (e.g. high-ET jets → gluon, W+/W– → sea quarks)


Full 3-loop (NNLO) non-singlet DGLAP splitting function!

Moch, Vermaseren and Vogt, hep-ph/0403192

new


14

15

16

17

18

19

20

21

22

23

24

partons: MRST2002NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. momentsNNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections

NLONNLO

LO

LHC Z(x10)

W

. B

l (

nb)

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

NNLONLO

LO

Tevatron (Run 2)

CDF D0(e) D0()

Z(x10)

W

CDF D0(e) D0()

. B

l (

nb)

LHC σNLO(W) (nb)

MRST2002 204 ± 4 (expt)

CTEQ6 205 ± 8 (expt)

Alekhin02 215 ± 6 (tot)

similar partons different Δχ2

different partons

σ(W) and σ(Z) : precision predictions and measurements at the LHC



ratio of W– and W+ rapidity distributions

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

MRST2002NLO ALEKHIN02NLO

d(W

- )/dy

/ d

(W+)/

dy

yW

x1=0.52 x2=0.000064

x1=0.006 x2=0.006

dû(W+)dû(Wà) = u(x1)dö(x2)+:::

d(x1)uö(x2)+:::

ratio close to 1 because u u etc.(note: MRST error = ±1½%)

–

sensitive to large-x d/u and small x u/d ratios

Q. What is the experimental precision?

––


pdfs from global fits

FormalismLO, NLO, NNLO DGLAPMSbar factorisationQ0

2

functional form @ Q02

sea quark (a)symmetryetc.

Who?Alekhin, CTEQ, MRST,GGK, Botje, H1, ZEUS,GRV, BFP, …

http://durpdg.dur.ac.uk/hepdata/pdf.html

DataDIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … )Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0)W rapidity asymmetry (CDF)N dimuon (CCFR, NuTeV)etc.

fi (x,Q2) fi (x,Q2)

αS(MZ )


summary of DIS data

+ neutrino FT DIS data Note: must impose cuts on

DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically:

Q2 > 2 - 4 GeV2

W2 = (1-x)/x Q2 > 10 - 15 GeV2


typical data ingredients of a global pdf fit


HEPDATA pdf server

Comprehensive repository of past and present polarised and unpolarised pdf codes (with online plotting facility) can be found at the HEPDATA pdf server web site:

http://durpdg.dur.ac.uk/hepdata/

pdf.html

… this is also the home of the LHAPDF project


(MRST) parton distributions in the proton

10-3

10-2

10-1

100

0.0

0.2

0.4

0.6

0.8

1.0

1.2

MRST2001

Q2 = 10 GeV

2

up down antiup antidown strange charm gluon

x

f(x,

Q2 )

x Martin, Roberts, S, Thorne

james stirling ippp, university of durham thanks to qcd-hard and qcd-soft parallel session...

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