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

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

proton
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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 production
jet production
NNLO QCD
NLO 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 s(Z) _at_ LHC
• ?spdf ? 3, ?spt ? 2
• ? ?stheory ? 4
• whereas for gg?H
• ?spdf ltlt ?spt

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not all NLO corrections are known!
the more external coloured particles, the more
difficult the NLO pQCD calculation Example pp
?ttbb X bkgd. to ttH
Nikitenko, Binn 2003
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John Campbell, Collider Physics Workshop, KITP,
January 2004
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NNLO the perturbative frontier

• The NNLO coefficient C is not yet known, the
  curves show guesses C0 (solid), CB2/A (dashed)
  ? the scale dependence and hence ? sth 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)

Tevatron jet inclusive cross section at ET 100
GeV
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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!

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summary of NNLO calculations

• p p ? jet X in progress, see previous
• p p ? ? 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 ? (?, W, Z) X van Neerven et al,
  Harlander and Kilgore corrected (2002)
• p p ? (?, 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

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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
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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 s(MH120 GeV) _at_ LHC
• ?spdf ? 3, ?sptNNL0 ? 10, ?sptNNLL ?
  8,
• ? ?stheory ? 9

Catani et al, hep-ph/0306211
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top quark production
awaits full NNLO pQCD calculation NNLO NnLL
softvirtual approximations exist (Cacciari et
al, Kidonakis et al), probably OK for Tevatron at
?10 level (gt ?spdf )
but such approximations work less well at LHC
energies
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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. MC_at_NLO)
• parton shower (e.g. HERWIG)

www.ippp.dur.ac.uk/HEPCODE/
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pdfs from global fits
Formalism NLO DGLAP MSbar factorisation Q02 functi
onal form _at_ Q02 sea quark (a)symmetry etc.
fi (x,Q2) ? ? fi (x,Q2)
aS(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.
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(MRST) parton distributions in the proton
Martin, Roberts, S, Thorne
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uncertainty in gluon distribution (CTEQ)
then ?fg ? ?sgg?X etc.
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solid LHC dashed Tevatron Alekhin 2002
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Higgs cross section dependence on pdfs
Djouadi Ferrag, hep-ph/0310209
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Djouadi Ferrag, hep-ph/0310209
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the differences between pdf sets needs to be
better understood!
Djouadi Ferrag, hep-ph/0310209
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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 ??2100,
  Alekhin ??21)
• factorisation/renormalisation scheme/scale
• Q02
• parametric form Axa(1-x)b.. etc
• aS
• 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
Z
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
aSn log(M2/qT2)m is necessary at small qT, to
be matched with fixed-order QCD at large qT

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• 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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aS measurements at hadron colliders

• in principle, from an absolute cross section
  measurement
• ? ? aSn
• but problems with exp. normalisation
  uncertainties, pdf uncertainties, etc.
• or from a relative rate of jet production
• ?(X jet) / ?(X) ? aS
• but problems with jet energy measurement,
  non-cancellation of pdfs, etc.
• or, equivalently, from shape variables (cf.
  thrust in ee-)

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S. Bethke
inclusive b cross section UA1, 1996
prompt photon production UA6, 1996
inclusive jet cross section CDF, 2002
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D0 (1997) R10 ?(W 1 jet) / ?(W 0 jet)
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BFKL at hadron colliders
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forward physics

• classical forward physics stot , sel , sSD,
  sDD, 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 or p p ? M ? X ? M
• where ? rapidity gap hadron-free zone, and X
  ?c, 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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rapidity gap collision events
Typical event
Hard single diffraction
Hard double pomeron
Hard color singlet
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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 ? 3s effect ?!
  
• Note calibration possible via X quarkonia or
  large ET jet pair

Observation of p p ? p ?0c (?J/? ?) p
by CDF?
QCD challenge to refine and test such models
elevate to precision predictions!
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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
  _at_ LEP)
• refining event simulation tools (e.g. PSNLO)
• 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
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• MRST Q02 1 GeV2, Qcut2 2 GeV2
• xg Axa(1x)b(1Cx0.5Dx)
• Exc(1-x)d
• CTEQ6 Q02 1.69 GeV2, Qcut2 4 GeV2
• xg Axa(1x)becx(1Cx)d

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tensions within the global fit?

• with dataset A in fit, ??21 with A and B in
  fit, ??2?
• 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

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CTEQ aS(MZ) values from global analysis with ??2
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 fixedorder
DGLAP insufficient for small-x DIS data?! ?
improvement in ?2 to remaining data / of data
points removed
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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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extrapolation errors
theoretical insight/guess f A x as x ? 0
theoretical insight/guess f A x0.5 as x
? 0
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differences between the MRST and Alekhin u and d
sea quarks near the starting scale
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s(W) and s(Z) precision predictions and
measurements at the LHC
LHC sNLO(W) (nb)
MRST2002 204 4 (expt)
CTEQ6 205 8 (expt)
Alekhin02 215 6 (tot)
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ratio of W and W rapidity distributions
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