Ill.Granular Source of QGP DropletsThe early system (QGP)produced in theAu+Au collisions atRHIC may be a strongly coupled medium with a very highenergy density. It is thermalized at a very early time before 1fm/c.The expansion ofthe system afterthattimemaybeunstableMany effect(the large fluctuations of initial energy distribution,surface tension, sound noise oflarge magnitudes accompanyinga highlyexplosiveexpansion,andphase transition)mayleadtoa fragmentationoftheveryhigh density system and theproduction of a granular source when it expands to vacuum.Although a granular structure was suggested earlier as thesignature of a first-order phase transition, the occurrence ofgranular structure may not belimited to a QGPmediumcharacterized by a first-order phase transition
III. Granular Source of QGP Droplets • The early system (QGP) produced in the Au + Au collisions at RHIC may be a strongly coupled medium with a very high energy density. It is thermalized at a very early time before 1 fm/c. • The expansion of the system after that time may be unstable. Many effect (the large fluctuations of initial energy distribution, surface tension, sound noise of large magnitudes accompanying a highly explosive expansion, and phase transition) may lead to a fragmentation of the very high density system and the production of a granular source when it expands to vacuum. • Although a granular structure was suggested earlier as the signature of a first-order phase transition, the occurrence of granular structure may not be limited to a QGP medium characterized by a first-order phase transition
InitialState Effect(a2015In many simulations of the heavy10ion collision on an event-by-eventbasis, the initial energy density isfar from being unifom and thereare large fluctuations of the initialdensitydistribution(a)Y.Hama,QM2005talk,hep-ph/0510096;(b)H.J.Drescher etal.PRC65.054902.2002.(NeXusmodel)These large density fluctua-tions in75the transverse direc-tion, togetherowith thesurface tension effects maylead to formation of granulardroplets!x [fm]
Initial State Effect In many simulations of the heavy ion collision on an event-by-event basis, the initial energy density is far from being uniform and there are large fluctuations of the initial density distribution. (a ) (b ) (a) Y. Hama, QM2005 talk, hep-ph /0510096; (b) H.J. Drescher et al., PRC65,054902,2002.(NeXus model) These large density fluctua-tions in the transverse direc-tion, together with the surface tension effects may lead to form ation of granular droplets!
220151510Model CalculationAveraging10ResultsFragmentationand formationModelPhysicsAveragingCalculationResultsofgranulardroplets★Comparingwithexperiments
Averaging Model Calculation Results Model Calculation Averaging Physics Results Fragmentation and formation of granular droplets Comparing with experiments
Based on the above picture, weuse a granular source model to des-元cribe the system after fragmenta-tion. Assume the droplets initiallydistribute in a shell of disk withanisotropic velocityZ(βa), = a, sgn(r)SR(i = x, y, z ). We use relativistichydrodynamics with the EOS ofRentropy density to describe theevolution of single droplet as we2Rdid. The evolution of the granularsource is obtained by superposingall of the droplet evolutionsexp[-(R, -p)? / △,] — shell factor
Based on the above picture, we use a granular source model to describe the system after fragmentation. Assume the droplets initially distribute in a shell of disk with anisotropic velocity (i = x, y, z ). We use relativistic hydrodynamics with the EOS of entropy density to describe the evolution of single droplet as we did. The evolution of the granular source is obtained by superposing all of the droplet evolutions. —— shell factor 2 2 exp[ ( ) / ] − − t t | | ( ) sgn( ) , i d i i i i b i r a r = π Z 2 z t
[)LoPhenixdataFig.1:Pion spectra of—a=0.30,a,=0.87transversemomentum10-10-2bIr(βa); = a, sgn(r)10-3Ra,=010-4a,=0.75Q31a,=0.82ar =(ax +a,) /2a,=0.8710-5Na =ax-a12300.51.52.5b, = 0.70, b. =0.01Pr (GeV/c)(PHENIXCollab.,PRC69,034909,2004
Fig. 1: Pion spectra of transverse momentum. ( ) / 2 T x y a a a = + T x y = − a a a 0.70, 0.01 T z b b = = (PHENIX Collab., PRC69, 034909, 2004.) | | ( ) sgn( ) , i d i i i i b i r a r =