outline of lectures lecture i: eft approach to high energy qcd-the color glass condensate;...
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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)
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Limiting fragmentation: Benecke, Chou, Yang, Yen
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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Solve classical Yang-Mills equations:
with two light cone sources
Proton source Nuclear source
Dumitru, McLerran; Blaizot, Gelis, RV
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 adjointrepresentation
=
Compute in CGC EFT
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Normalization:
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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
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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
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A) BK equation for the unintegrated distribution:
Non-linear equation for dipole amplitude
BFKL kernel
U’s in fund. rep.
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Large Nc limit:
F.T. ofdipoleamplitude
Above equation
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Initial conditions for BK evolution:
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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
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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
MV+frag.function
UA1 data averagedover y=0.0-2.5
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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
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Extrapolation to LHC:
Estimated charged particle multiplicity ~ 1000-1500
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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
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MV
MV + frag. func.
Pt distribution:
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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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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
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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
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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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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