QCD: from the Tevatron to the LHC

James Stirling

IPPP, University of Durham

• Overview

• Perturbative QCD – precision physics

• ‘Forward’ (non-perturbative) processes

• Summary

Forum04 2

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!

Forum04 3

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

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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

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examples of ‘precision’ phenomenology

W, Z productionjet production

NNLO QCDNLO QCD

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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

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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)

4% total error(MRST 2002)

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t

tb

b

Nikitenko, Binn 2003

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

Example: pp →ttbb + Xbkgd. to ttH

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John Campbell, Collider Physics Workshop, KITP, January 2004

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NNLO: the perturbative frontierThe 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

Forum04 10

jets at NNLO• 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

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

soft, collinear

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summary of NNLO calculations• p + p → jet + X *; in progress, see previous• p + p → γ + X; in principle, subset of the jet calculation

but issues regarding photon fragmentation, isolation etc• p + p → QQbar + X; requires extension of above to non-

zero fermion masses• p + p → (γ*, W, Z) + X *; van Neerven et al, Harlander and

Kilgore corrected (2002)

• p + p → (γ*, W, Z) + X differential rapidity distribution *; Anastasiou, Dixon, Melnikov (2003)

• p + p → H + X; Harlander and Kilgore, Anastasiou and Melnikov (2002-3)

Note: knowledge of processes * needed for a full NNLO global parton distribution fit

Forum04 12

+

interfacing NnLO and parton showers

Benefits of both:

NnLO correct overall rate, hard scattering kinematics, reduced scale, dependence, …

PS complete event picture, correct treatment of collinear logarithms to all orders, …

→ see talk by Bryan Webber

Forum04 13

HO corrections to Higgs cross section

Catani et al, hep-ph/0306211

• 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

Forum04 14

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

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• 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/

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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 )

Forum04 17

(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

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uncertainty in gluon distribution (CTEQ)

then fg → σgg→X etc.

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solid = LHCdashed = Tevatron

Alekhin 2002

pdf uncertainties encoded in parton-parton luminosity functions:

with = M2/s, so that for ab→X

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10-7

10-6

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10-1

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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

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-410

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010

0

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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

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Djouadi & Ferrag, hep-ph/0310209

Higgs cross section: dependence on pdfs

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Djouadi & Ferrag, hep-ph/0310209

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

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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

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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

Bozzi Catani de FlorianGrazzini

qT (GeV)

KuleszaStermanVogelsang

Z

Forum04 26

• 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

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αS measurements at hadron colliders

• in principle, from an absolute cross section measurement…

αSn

but problems with exp. normalisation uncertainties, pdf uncertainties, etc.

• or from a relative rate of jet production(X + jet) / (X) αS

but problems with jet energy measurement, non-cancellation of pdfs, etc.

• or, equivalently, from ‘shape variables’ (cf. thrust in e+e-)

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inclusive bcross sectionUA1, 1996

prompt photonproductionUA6, 1996

inclusive jetcross sectionCDF, 2002

S. Bethke

hadron collider measurements {

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D0 (1997): R10= (W + 1 jet) / (W + 0 jet)

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BFKL at hadron collidersAndersen, WJS

jetjet

Production of jet pairs with equal and opposite large rapidity (‘Mueller-Navelet’ jets) as a test of QCD BFKL physics

cf. F2 ~ x as x →0 at HERA

many tests:

• y dependence, azimuthal angle decorrelation, accompanying minjets etc

• replace forward jets by forward W, b-quarks etc

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forward physics• ‘classical’ forward physics – σtot , σel , σSD, σDD, etc – a challenge for non-

perturbative QCD models. Vast amount of low-energy data (ISR, Tevatron, …) to test and refine such models

• output → deeper understanding of QCD, precision luminosity measurement (from optical theorem L ~ Ntot

2/Nel)

• ‘new’ forward physics – a potentially important tool for precision QCD and New Physics Studies at Tevatron and LHC

p + p → p X p or p + p → M X M

where = rapidity gap = hadron-free zone, and X = χc, H, tt, SUSY particles, etc etc

advantages? good MX resolution from Mmiss (~ 1 GeV?) (CMS-TOTEM)

disadvantages? low event rate – the price to pay for gaps to survive the ‘hostile QCD environment’

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Typical event

Hard single diffraction

Hard double pomeron

Hard color singlet

‘rapidity gap’ collision events

DD

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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 ?!

Note: calibration possible via X = quarkonia or large ET jet pair

Observation of

p + p → p + χ0c (→J/ γ) + p

by CDF?

new

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

selection rules

couples to gluons

Forum04 35

summary

‘QCD at hadron colliders’ means …

• performing precision calculations (LO→NLO→NNLO ) for signals and backgrounds, cross sections and distributions – still much work to do! (cf. EWPT @ LEP)

• refining event simulation tools (e.g. PS+NLO)

• extending the calculational frontiers, e.g. to hard + diffractive/forward processes, multiple scattering, particle distributions and correlations etc. etc.

• particularly important and interesting is p + p → p X p – challenge for experiment and theory

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extra slides

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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)

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

Moch, Vermaseren and Vogt, hep-ph/0403192

new

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• MRST: Q02 = 1 GeV2, Qcut

2 = 2 GeV2

xg = Axa(1–x)b(1+Cx0.5+Dx)

– Exc(1-x)d

• CTEQ6: Q02 = 1.69 GeV2,

Qcut2 = 4 GeV2

xg = Axa(1–x)becx(1+Cx)d

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2

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0.25

0.50

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1.00

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1.75

2.00

Experiment B

Experiment A

systematic error

systematic error

measurement #

• with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=? • ‘tensions’ between data sets arise, for example,

– between DIS data sets (e.g. H and N data) – when jet and Drell-Yan data are combined with DIS data

tensions within the global fit?

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CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100

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as small x data are systematically removed from the MRST global fit, the quality of the fit improves until stability is reached at around x ~ 0.005 (MRST hep-ph/0308087)

Q. Is fixed–order DGLAP insufficient for small-x DIS data?!

Δ = improvement in χ2 to remaining data / # of data points removed

Forum04 43

the stability of the small-x fit can be recovered by adding to the fit empirical contributions of the form

... with coefficients A, B found to be O(1) (and different for the NLO, NNLO fits); the starting gluon is still very negative at small x however

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0.01 0.1 1-4

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f(x)

x0.01 0.1 1

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f(x)

x0.01 0.1 1

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f(x)

x

extrapolation errors

theoretical insight/guess: f ~ A x as x → 0

theoretical insight/guess: f ~ ± A x–0.5 as x → 0

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differences between the MRST and Alekhin u and d sea quarks near the starting scale

ubar=dbar

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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

4% total error(MRST 2002)

Forum04 48

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?

––

Forum04 49

Note: high-x gluon should become better determined from Run 2 Tevatron dataQ. by how much?

Note: CTEQ gluon ‘more or less’ consistent with MRST gluon