Gluon PDF at LHC

1
Gluon PDF at LHC

• Hideki Hamagaki
• Center for Nuclear Study
• University of Tokyo

2
Initial Processes in High-Energy Heavy-Ion
Collisions

• Collisions in high energy
• between partons (quarks and gluons) in the
  colliding nucleons
• Two competing processes in the initial stage
• soft process
• dominant in the low-energy collisions
• multi-particle production with low-pT
• non-perturbative
• hard process
• large-Q2 scattering between partons
• pQCD calculation
• becomes prominent in high energy

3
Hard Collisions

• Many jets in central PbPb collisions at LHC
• Dnjet/Dh 1.7 x N(coll) 1700
• In sharp contrast to RHIC, where Dn/Dh 0.2 x
  N(coll)
• without gluon shadowing effect
• Mini-jets with relatively low energy are dominant
  
• collisions between small-x gluons
• Fraction of harder jets grows with collision
  energy
• this tendency is even so with gluon saturation
  effect

4
A general comment on Initial Collisions at LHC

• Complication of initial state
• A large number of energetic partons
• How much of the energy spent for collisions is
  used to form the medium in the initial stage
• Space-time evolution may also become complicated
• a part of lost energy may be used to heat up the
  fluid, while other part may simply escape the
  system
• A honeymoon between QGP and Hydro may be
  disturbed more often at LHC with intruding jets
  even in the bottom-up scenario
• This should be a quantitative question hopefully
  to be answered before having collisions at LHC

5
Initial state elements PDFs
Before the collision. Initial state
6
Hard scattering elements partonic two-body
subprocesses
QCD partonic two-body subprocesses (perturbative,
LO).
7
Final state FFs
After (hard) collision. Final state

• Fragmentation functions
• (non-perturbative, LO) probability density for a
  parton k, which will finally fragments into
  hadron h, carrying the fraction z of the momentum
  of pT parent parton.

8
Characteristics of Hard Process

• Production of jet, hard photon, heavy quarks, ...
• hard collision (large Q2) between partons,
  descibed with pQCD
• production yield is proportional to number of
  collisions between nucleons
• with known nuclear effects
• Nuclear modification of parton distribution
  function (PDF)
• Cronin effect
• Nuclear modification factor

9
Nuclear Effects

• Nuclear modification of PDF
• shadowing/anti-shadowing, depending on x
  (fraction of momentum carried by a parton)
• Cronin effect
• spA(pT) spp(pT) Aa(pT)
• a (pT) gt 1 in the high pT
• small-angle multiple scattering of partons in the
  initial stage
• kT broadening

10
Deep Inelastic Scattering at HERA

• DIS
• F2(x,Q2)
• dominant over most of the phase space
• rise strongly at small Bjorken-x
• F2 scaling violation -- increase of gluon
  radiation from sea quarks

M. Dittmar et al., hep-ph/0511119
lt- logarithmically rising with Q2
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Gluon Distribution

• PDF evolution with Q2
• a value at any Q2 is calculable from the value
  measured at Q02 with the DGLAP (Dokshitzer-Gribov-
  Lipatov-Altareli-Parisi) evolution equation
• pQCD calculation for parton branching (gluon
  splitting, q,g-strahlung)
• ln(Q2) gtgt ln(1/x)
• PDF evolution with x at a fixed Q2 in small x
• the BFKL (Balitski-Fadin-Kuraev-Lipatov) equation

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(x,Q2) Evolution of PDF

• Q2 evolution (kT-ordered emission) DGLAP
  evolution equation
• Dokshitzer-Gribov-Lipatov-Altareli-Parisi
• x evolution (pL-ordered emission) BFKL equation
• Balitski-Fadin-Kuraev-Lipatov

13
Non-linear Effect and Saturation of Parton
Density at low x

• Gluon density becomes very high at low x -gt
  non-linear (g-g fusion) effect becomes important,
  which tames the growth of the parton densities
• standard DGLAP and BFKL linear equation are not
  applicable
• pQCD factorization should break, because of
  assumption of incoherent parton scattering
• pQCD calculations -gt unitarity violation
• Saturation scale Qs

number of gluons with transverse area r2 1/Q2
14
Nuclear Number Dependence of Saturation Scale

• Sizable A dependence
• End of independent particle description of
  partons
• Saturation Scale

15
Nuclear Modification of Low-x Gluon PDF

• Current knowledge of low-x gluons
• nuclear F2, nuclear Drell-Yan (p-A), high-pT
  hadrons (d-Au_at_RHIC)
• Nuclear xG(x,Q2) below x 10-2 is very
  uncertain -gt LHC could be an ideal machine to
  investigate this

16
Initial state elements PDFs

• Jet-jet rapidity correlation (Dy 3)
• Yield of inclusive jet or energetic particles at
  a certain y are sum of contributions from
  different x
• PDF information for wide x range is needed

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Rough Idea of x at RHIC and LHC

• J/y in dAu (s1/2 200 GeV) _at_ PHENIX
• 2.2ltylt1.2 x0.09
• y0 x0.02
• -1.2 ltylt-2.2 x3 x 10-3
• LHC
• y -2 x 5 x 10-3
• y 0 x 7 x 10-4
• y 2 x 1 x 10-4

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A Hint from RHIC data -I-

• Collision energy dependence of global
  multiplicity in Au Au collisions, by PHOBOS
  (NPA757(2005)28)
• Lines are with a saturation model by Armesto, N
  et al. (PRL94(2005)022002)

19
A Hint from RHIC data -II-

• High pT hadrons from d Au by BRAHMS
  (NPA757(2005)1)
• RdAu 0.8 at h 3.2, pT 3 GeV/c ( x 10-3)
• CGC model
• Kharzeev, D et al. (PLB599(2004)23)
• Jalilian-Marian, J. (NPA748(2005)664)
• Sizable PDF modification could be possible even
  at central rapidity in LHC
• y 0, pT 3 GeV/c ( x 10-3)
• RdAu 0.8 -gt RPbPb (0.8)2 0.6
• pA data is crucial, probably more than at RHIC
• uncertain gluon PDF at low x
• interpretation of RAA needs RpA

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Single leptons in dAu

• Cold nuclear matter (CNM) effects
• Shadowing Cronin effect
• PHENIX Muon results from 2003 dAu
• RdAu gt 1 for south (x2 is large)
• RdAu lt 1 for north (x2 is small)
• High statistics dAu data is needed, and Run08
  results will be available soon.

Eskola et al. NPA696 (2001) 729
south arm Au going
north arm d going
Au going d going
south
north
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Cold Nuclear Matter effect of J/y at RHIC--
studied with dAu --

• Gluon PDF for nuclei
• largely ambiguous
• dAu data was analyzed with the model
  calculations (EKS NDSG model), to obtain sabs
  2 3 mb
• still large error bars

J/y in dAu _at_ PHENIX -2.2ltylt-1.2 x0.09
y0 x0.02 1.2 ltylt2.2 x0.003
PHENIX PRC 77, 024912 (2008)
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CNM effects in AuAu

• Extrapolated from dAu collisions
• J/y suppression beyond the CNM effects
• although error bars for both AuAu results and
  CNM effect are large

PHENIX PRC 77, 024912 (2008)
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Summary

• Understanding the initial state (even before
  collision) will be more crucial to understand the
  results at LHC than at RHIC
• Few experimental data and wide-spreading
  theoretical predictions for nuclear Gluon PDF
• Evolution and possible saturation of gluon PDF
  itself is an interesting subject
• Why not mapping them out!?