onset of thermal equilibration

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Traces of
Thermalization at RHIC
Sean Gavin
Wayne State University

• onset of thermal equilibration common
  centrality dependence of ?pt?, pt and charge
  dynamic fluctuations

• I. Fluctuations from nonequilibrium two-body
  correlations
• multiplicity and pt fluctuation observables
• approach to equilibrium
• initial and near-equilibrium fluctuations
• II. Experiments
• PHENIX and STAR mean pt and fluctuations
• energy dependence, net charge fluctuations

nucl-th/0308067
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Dynamic Fluctuations
Pruneau, Voloshin S.G.
variance minus thermal contribution
multiplicity N mean pt

• probe two-body correlation function

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(No Transcript)
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Time Scales
initially string fragmentation

• later clumps, size ? ?
• local thermalization time ? ?-1
• scattering rate ? ? ?? vrel?n

• much later (if ever)
• flow between clumps ?
• homogeneity
• diffusion time tdiff ? ??2

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Fluctuation Sources
dynamic fluctutations (strings)-1
dynamic fluctutations (clumps)-1 -- larger?
depends on clump size
Gazdzicki Mrowczynski
statistical fluctuations (particles)-1 dynamic
fluctuations vanish
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Partial Thermalization
random walk n collisions
collision many walkers bouncing off each other
energy conservation limits pt increase Boltzmann
equation ?
survival probability
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Nonequilibrium ?pt?
central collisions more participants N longer
lifetime ? smaller survival probability S
Boltzmann equation longitudinal expansion

• survival probability
• equilibrium cooling
• centrality dependence

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Nonequilibrium Dynamic Fluctuations
Boltzmann equation with Langevin noise ?
phase-space correlations ? dynamic fluctuations
simple limits independent initial and near-local
equilibrium correlations initial correlations
equilibrium-like
same centrality dependence of S
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Initial and Near-Local Equilibrium Fluctuations

• initial fluctuations
• M participant nucleons
• ? independent strings

near equilibrium correlations from clumpiness
more likely to find particles near hot spots ?
spatial correlation function r(x1,x2)
transverse size Rt, correlation length ?
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Nonequilibrium Fluctuations
initial fluctuations wounded nucleons
near equilibrium correlation length ? 1 fm R
? N1/2
survival probability centrality dependence from
?pt? data
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Energy Dependence
multiplicity, scattering rate ? ? dN/d?, RAA ?
(dN/d?) -1
FIND partial thermalization describes
trends. Deviation in central collisions at
highest energies jets?
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Similar Charge Fluctuations
expect same charge fluctuations ? correlations
r(p1,p2)

• rapidity correlation length
• ??rms 0.5 in AA
• ??rms 1 in pp
• consistent with balance function
• measurements

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Fluctuations not just for Exotic Phenomena!
Summary Partial Thermalization

• ?pt?, pt and charge fluctuations
• common behavior peripheral
• but alternative indivdual explanations
  
• central collisions?
• cooling? PHENIX yes, STAR no
• jet contribution to fluctuations?
• partons or hadrons?
• species independence for ?pt?
• need particle-identified fluctuations

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Initial Fluctuations

• AA collision
• M participant nucleons
• ? independent strings
• multiplicity ? M
• variance
• RAA ? M-1
• dynamic pt fluctuations

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Fluctuations Near Equilibrium
correlations from non-uniformity more likely to
find particles near hot spots ? spatial
correlation function

• assume
• longitudinal Bjorken expansion
• uncorrelated longitudinal and transverse d.o.f.'s
• ?pt ? ?T(x) independent of rapidity
• gaussian densities, correlation function

obtain
transverse size Rt, correlation length ?
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Approach to Equilibrium
Boltzmann Equation for phase space density f(x,p)
approximation relaxation time ??? Bjorken
scaling Baym Gavin B. Zhang Gyulassy

where pz' pz(t/t0)
survival probability chance of no scattering
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Nonequilibrium Fluctuations

• Introduce fluctuations
• Boltzmann Equation plus Langevin noise
• Langevin noise for f e
• relaxation equation for correlation functions
• obtain
• Bjorken flow

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Near Local Equilibrium Correlations
single particle
particle correlations