Transcript Multi-particle production in QCD at high energies

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)
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:
Dumitru, McLerran;
Blaizot, Gelis, RV
with two light cone sources
Proton source
Lorentz gauge:
Nuclear source
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:
Compute in CGC EFT
with the path ordered exponentials in the adjoint
representation
=
Normalization:
First, a qualitative explanation of LF:
Small x-black disc-unitary limitNo dependence on x_2 = y+ y_beam
Large x-dilute projectile
When
From unitarity
of the U matrices
~ Bj. Scaling => independent of x_2
J. Jalilian-Marian
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
A) BK equation for the unintegrated distribution:
Non-linear equation for dipole amplitude
BFKL kernel
U’s in fund. rep.
Large Nc limit:
Above
equation
F.T. of
dipole
amplitude
Initial conditions for BK evolution:
Parameters:
From quark counting rules
Take zero for AA-may need finite value
for pp
Regulates log. Infrared divergence
(same value in \eta -> y conversion)
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 averaged
over y=0.0-2.5
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
Extrapolation to LHC:
Estimated charged particle multiplicity ~ 1000-1500
dN/deta extrapolations to LHC
Central Pb+Pb collisions at LHC energy
Assuming: dN/dh grows log(s) and linear scaling at high h holds
M. Nardi
W. Busza
ALICE Tech. Proposal,
M. Nardi, various models and fits
Acta Phys.Polon.B35 2873 (2004 )
Gabor Veres, QM2005
Pt distribution:
MV
MV + frag. func.
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
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:
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
Interpretation:
Blaizot, Gelis, RV; Tuchin
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.
Results in the MV model: multi-scattering effects
Collinear logs:
LO in pQCD
NLO in pQCD
Relation to 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
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.