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I. Fluctuations from nonequilibrium two-body correlations

Traces of Thermalization at RHIC Sean Gavin Wayne State University. onset of thermal equilibration – common c entrality dependence of p t , p t and charge dynamic fluctuations. I. Fluctuations from nonequilibrium two-body correlations

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I. Fluctuations from nonequilibrium two-body correlations

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  1. Traces of Thermalizationat RHICSean 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 andfluctuations • energy dependence, net charge fluctuations nucl-th/0308067

  2. Dynamic Fluctuations Pruneau, Voloshin & S.G. variance minus thermal contribution multiplicity N mean pt probe two-body correlation function:

  3. Equivalent! Fpt  pt/  pt/  Npt1pt22 2

  4. 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

  5. Fluctuation Sources dynamic fluctutations ~ (strings)-1 dynamic fluctutations ~ (clumps)-1 -- larger? depends on clump size Gazdzicki & Mrowczynski statistical fluctuations ~ (particles)-1 dynamic fluctuations vanish

  6. few collisions many collisions – saturates at Partial Thermalization random walk – n collisions collision: many walkers bouncing off each other – energy conservation limits pt increase Boltzmann equation  survival probability:

  7. Nonequilibrium pt central collisions: more participants N longer lifetime  smaller survival probability S Boltzmann equation + longitudinal expansion • survival probability • equilibrium cooling • centrality dependence

  8. 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 samecentrality dependence of S

  9. 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 

  10. Nonequilibrium Fluctuations initial fluctuations – wounded nucleons near equilibrium correlation length  ~ 1 fm; R  N1/2 survival probability centralitydependence fromptdata

  11. Energy Dependence multiplicity, scattering rate   dN/d, RAA (dN/d) -1 FIND: partial thermalization describes trends. Deviation in central collisions at highest energies – jets?

  12. 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

  13. Summary: Partial Thermalization Fluctuations: not just for Exotic Phenomena! 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 • needparticle-identified fluctuations

  14. Initial Fluctuations AA collision: M participant nucleons  independent strings multiplicity  M variance RAA  M-1 dynamic pt fluctuations

  15. 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 

  16. 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

  17. Nonequilibrium Fluctuations Introduce fluctuations: • Boltzmann Equation plus Langevin noise • Langevin noise for f e relaxation equation for correlation functions obtain: Bjorken flow:

  18. density correlations momentum correlations temperature correlations Near Local Equilibrium Correlations single particle: particle correlations

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