Multi-particle production in QCD at high energies

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(No Transcript)
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Outline of Lectures

• Lecture I EFT approach to high energy QCD-The
  Color Glass Condensate
• multi-particle production in the CGC
• Lecture II Hadronic scattering in the CGC
• - multiple scattering quantum evolution
  effects
• in limiting fragmentation quark pair
  production
• Lecture III Plasma instabilities
  thermalization
• in the CGC computing particle production in
• Heavy Ion collisions to next-to-leading order
  (NLO)

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Benecke, Chou, Yang, Yen
Limiting fragmentation
PHOBOS
Work motivated by A. Bialas and M. Jezabek
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Proton-Nucleus collisions in the Color Glass
Condensate
Power counting may also be applicable in AA
collisions in the fragmentation regions
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Dumitru, McLerran Blaizot, Gelis, RV
Solve classical Yang-Mills equations
with two light cone sources
Proton source
Nuclear source
Lorentz gauge
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Systematically truncate equations to lowest order
in
and all orders in
to obtain gauge field
Compute the k_perp factorized inclusive
multiplicity
M. Braun Kharzeev, Kovchegov, Tuchin Blaizot,
Gelis, RV
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Unintegrated distribution
with the path ordered exponentials in the
adjoint representation

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Normalization
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First, a qualitative explanation of LF
Small x-black disc-unitary limit- No dependence
on x_2 y y_beam
Large x-dilute projectile
When
From unitarity of the U matrices
Bj. Scaling gt independent of x_2
J. Jalilian-Marian
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Gelis, Stasto, RV
Detailed analysis
A) Solve RG (in x) equations for unintegrated
gluon distributions- consider the
Balitsky-Kovchegov (BK) mean field equation
(large Nc and large A limit of general
expression in the CGC) B) Compute inclusive
distributions and compare to data from pp, D-A
and AA collisions for different initial
conditions
Similar in spirit to previous work of Kharzeev,
Levin, Nardi
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A) BK equation for the unintegrated
distribution
Non-linear equation for dipole amplitude
BFKL kernel
Us in fund. rep.
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Large Nc limit
Above equation
F.T. of dipole amplitude
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Initial conditions for BK evolution
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Parameters
From quark counting rules
Take zero for AA-may need finite value for pp
Regulates log. Infrared divergence (same value
in \eta -gt y conversion)
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B) Results
Note assume Parton-Hadron duality initially -
shall discuss effects of fragmentation later
i) PP collisions
UA5 data
PHOBOS data
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Limiting fragmentation in pp from MV/GBW BK
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Extrapolation to LHC
Extrapolation with GBW initial conditions -MV is
much flatter
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Cut-off dependence
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P_t distribution-effect of fragmentation
functions
MV
GBW
MVfrag.function
UA1 data averaged over y0.0-2.5
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ii) AA collisions
PHOBOS
Filled triangles, squares circles
BRAHMS
Open triangles, squares circles
Data at c.m energies Of 19.6, 130, 200 GeV/n
STAR
Data at 62.4 GeV/n
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Extrapolation to LHC
Estimated charged particle multiplicity
1000-1500
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dN/deta extrapolations to LHC
Central PbPb collisions at LHC energy
Assuming dN/dh grows ?log(s) and linear scaling
at high h holds
Acta Phys.Polon.B35 2873 (2004 )
Gabor Veres, QM2005
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Pt distribution
MV
MV frag. func.
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iii) D-Au collisions
PHOBOS
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Summary of LF discussion

• In the kt factorization framework, LF follows
  from
• Saturation of unitarity constraint in the
  target
• wavefunction-black disc limit.
• Bjorken scaling at large x
• Deviations from LF test QCD evolution equations
• (caveat large x extrapolations matter)
• Fragmentation function effects important for
  better
• agreement with data
• at higher energies (study in progress). Need
  to
• quantify deviations from kt factorization as
  well.

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Quark pair production in pA collisions
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Pair cross-section
Amputated time ordered quark propagator in
classical background field
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Blaizot, Gelis, RV
Result not kt factorizable in general -can
however be factorized into novel multi-parton
distributions

• These multi-parton distributions can be computed
• in closed form in Gaussian (MV) approximation
• - study multiple scattering effects
• b) Quantum evolution of distributions determined
• by JIMWLK or BK RG eqns.
• - study shadowing effects as well

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Blaizot, Gelis, RV Tuchin
Interpretation
Wilson line correlators - the last appears in
pair production only
Simplify greatly in large N_c limit x-evolution
can be computed with Balitsky-Kovchegov eqn.
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Results in the MV model multi-scattering effects
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Collinear logs
Relation to pQCD
LO in pQCD
NLO in pQCD
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R_pA suppression
Frankfurt, Strikman Matsui, Fujii
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Rapidity dist. of pairs from BK evolution
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R_pA from BK
Dots denote region uncontaminated by large x
extrapolation
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R_pA vs Y
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Solve Dirac equation in background field of two
nuclei
Gelis,Kajantie,Lappi PRL 2005
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Ratio of quarks to glue roughly consistent with a
chemically equilibrated QGP at early times
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Outlook
We can compute both small x evolution (shadowing)
and multiple scattering effects in quark
production on same footing. More detailed
studies in progress for D-Au collisions
Quark production in AA collisions can be
computed at the earliest stages.