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QCD: from the Tevatron to the LHC

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### QCD: from the Tevatron to the LHC

James Stirling

IPPP, University of Durham

- Overview
- Perturbative QCD – precision physics
- ‘Forward’ (non-perturbative) processes
- Summary

Model, Fit, Extrapolate & Pray!

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

Forum04

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

jet

P

x1P

x2P

P

antiproton

jet

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

^

proton

Forum04

momentum fractions x1 and x2determined by mass and rapidity of X

xdependence 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

Forum04

(MRST 2002)

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

Forum04

not all NLO corrections are known!

t

b

t

b

the more external coloured particles, the more difficult the NLO pQCD calculation

Example:

pp →ttbb + X

bkgd. to ttH

Nikitenko, Binn 2003

Forum04

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

Tevatron jet inclusive cross section at ET = 100 GeV

Forum04

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!

Forum04

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

interfacing NnLO and parton showers

Benefits of both:

NnLOcorrect overall rate, hard scattering kinematics, reduced scale, dependence, …

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

→ see talk by Bryan Webber

Forum04

H

t

g

HO corrections to Higgs cross section- 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%

Catani et al,

hep-ph/0306211

Forum04

NNLO(S+V)

NLO

LO

Kidonakis and Vogt, hep-ph/0308222

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 )

… but such approximations work less well at LHC energies

Forum04

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

- 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. [email protected])
- parton shower (e.g. HERWIG)

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

Forum04

Alekhin, CTEQ, MRST,

GKK, Botje, H1, ZEUS,

GRV, BFP, …

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

pdfs from global fitsFormalism

NLO DGLAP

MSbar factorisation

Q02

functional form @ Q02

sea quark (a)symmetry

etc.

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

αS(MZ )

Data

DIS (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.

Forum04

pdf uncertainties encoded in parton-parton luminosity functions:

with = M2/s, so that for ab→X

solid = LHC

dashed = Tevatron

Alekhin 2002

Forum04

Djouadi & Ferrag, hep-ph/0310209

Forum04

the differences between pdf sets needs to be better understood!

Djouadi & Ferrag, hep-ph/0310209

Forum04

why do ‘best fit’ pdfs and errors differ? understood!

- 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

Forum04

Kulesza understood!

Sterman

Vogelsang

qT (GeV)

Bozzi

Catani

de Florian

Grazzini

resummationZ

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/qT2)m

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

Forum04

- 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)/dqTprovides good test of calculations

Forum04

α Higgs (MS 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-)

Forum04

hadron collider Higgs (M

measurements

{

S. Bethke

inclusive b

cross section

UA1, 1996

prompt photon

production

UA6, 1996

inclusive jet

cross section

CDF, 2002

Forum04

Forum04 Higgs (M

D0 (1997): Higgs (MR10= (W + 1 jet) / (W + 0 jet)

Forum04

- 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

Andersen, WJS

jet

jet

BFKL at hadron collidersForum04

forward physics rapidity (‘Mueller-Navelet’ jets) as a test of

- ‘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 ~ Ntot2/Nel)
- ‘new’ forward physics – a potentially important tool for precision QCD and New Physics Studies at Tevatron and LHC
p + p → p X p orp + 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’

Forum04

‘rapidity gap’ collision events rapidity (‘Mueller-Navelet’ jets) as a test of

Typical event

Hard single diffraction

Hard double pomeron

Hard color singlet

Forum04

couples to gluons rapidity (‘Mueller-Navelet’ jets) as a test of

new

selection rules

- 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?

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

Forum04

summary rapidity (‘Mueller-Navelet’ jets) as a test of

‘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

Forum04

extra slides rapidity (‘Mueller-Navelet’ jets) as a test of

Forum04

pdfs at LHC rapidity (‘Mueller-Navelet’ jets) as a test of

- 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)

Forum04

new rapidity (‘Mueller-Navelet’ jets) as a test of

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

Moch, Vermaseren and Vogt, hep-ph/0403192

Forum04

- MRST: Q rapidity (‘Mueller-Navelet’ jets) as a test of 02 = 1 GeV2,Qcut2 = 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

Forum04

tensions within the global fit? rapidity (‘Mueller-Navelet’ jets) as a test of

- 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

Forum04

CTEQ rapidity (‘Mueller-Navelet’ jets) as a test of αS(MZ) values from global analysis with Δχ2 = 1, 100

Forum04

as small rapidity (‘Mueller-Navelet’ jets) as a test of 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

the stability of the small- rapidity (‘Mueller-Navelet’ jets) as a test of 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

Forum04

extrapolation errors rapidity (‘Mueller-Navelet’ jets) as a test of

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

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

Forum04

ubar=dbar rapidity (‘Mueller-Navelet’ jets) as a test of

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

Forum04

Forum04 rapidity (‘Mueller-Navelet’ jets) as a test of

different partons rapidity (‘Mueller-Navelet’ jets) as a test of

4% total error

(MRST 2002)

similar partons

different Δχ2

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

Forum04

x rapidity (‘Mueller-Navelet’ jets) as a test of 1=0.006

x2=0.006

–

x1=0.52

x2=0.000064

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?

–

–

ratio of W–and W+ rapidity distributions

Forum04

Note: rapidity (‘Mueller-Navelet’ jets) as a test of CTEQ gluon ‘more or less’ consistent with MRST gluon

Note:high-x gluon should become better determined from Run 2 Tevatron data

Q. by how much?

Forum04

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