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Outline of LecturesLecture 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)
Limiting fragmentation: Benecke, Chou, Yang, Yen
PHOBOS
Work motivated by A. Bialas and M. Jezabek
Proton-Nucleus collisions in the Color Glass Condensate
Power counting may also be applicable in AA collisions in the fragmentation regions
Solve classical Yang-Mills equations:
with two light cone sources
Proton source Nuclear source
Dumitru, McLerran; Blaizot, Gelis, RV
Lorentz gauge:
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
Unintegrated distribution:
with the path ordered exponentials in the adjointrepresentation
=
Compute in CGC EFT
Normalization:
First, a qualitative explanation of LF:
Large x-dilute projectile
Small x-black disc-unitary limit-No dependence on x_2 = y+ y_beam
When
From unitarity of the U matrices
~ Bj. Scaling => independent of x_2J. Jalilian-Marian
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
Gelis, Stasto, RV
A) BK equation for the unintegrated distribution:
Non-linear equation for dipole amplitude
BFKL kernel
U’s in fund. rep.
Large Nc limit:
F.T. ofdipoleamplitude
Above equation
Initial conditions for BK evolution:
Parameters:
From quark counting rules
Regulates log. Infrared divergence (same value in \eta -> y conversion)
Take zero for AA-may need finite value for pp
B) Results:
Note: assume Parton-Hadron duality initially - shall discuss effects of fragmentation later
i) PP collisions:
UA5 data:
PHOBOS data:
Limiting fragmentation in pp from MV/GBW + BK
Extrapolation to LHC
Extrapolation with GBW initial conditions-MV is much flatter
Cut-off dependence:
P_t distribution-effect of fragmentation functions:
MV
GBW
MV+frag.function
UA1 data averagedover y=0.0-2.5
ii) AA collisions:
PHOBOS
Data at c.m energiesOf 19.6, 130, 200 GeV/n
Filled triangles, squares & circles
BRAHMS
Open triangles, squares & circles
STAR
Data at 62.4 GeV/n
Extrapolation to LHC:
Estimated charged particle multiplicity ~ 1000-1500
dN/deta extrapolations to LHCCentral Pb+Pb collisions at LHC energy Central Pb+Pb collisions at LHC energy
Assuming: dN/d grows log(s) and linear scaling at high holds
Acta Phys.Polon.B35 2873 (2004 )
M. NardiM. Nardi W. BuszaW. Busza
ALICE Tech. Proposal,M. Nardi, various models and fits
Gabor Veres, QM2005
MV
MV + frag. func.
Pt distribution:
iii) D-Au collisions:
PHOBOS
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.
Quark pair production in pA collisions
= …
Pair cross-section:
Amputated time ordered quark propagator in classical background field
Result not kt factorizable in general -can however be “factorized” into novel multi-parton distributions
These multi-parton distributions can be computed:
a) 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
Blaizot, Gelis, RV
Interpretation:
Wilson line correlators - the last appears in pair productiononly
Simplify greatly in large N_c limit x-evolution can be computed with Balitsky-Kovchegov eqn.
Blaizot, Gelis, RV; Tuchin
Results in the MV model: multi-scattering effects
Collinear logs: Relation to pQCD
LO in pQCD
NLO in pQCD
R_pA: suppression
Frankfurt, Strikman; Matsui, Fujii
Rapidity dist. of pairs from BK evolution
R_pA from BK:
Dots denote region “uncontaminated” by large x extrapolation
R_pA vs Y:
Solve Dirac equation in background field of two nuclei…
Gelis,Kajantie,Lappi PRL 2005
Ratio of quarks to glue roughly consistent with a chemically equilibrated QGP at early times
Quark production in AA collisions can be computed at the earliest stages.
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