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