Elliptic flow and incomplete equilibration in AMPT JianLi

Elliptic flow and incomplete equilibration in AMPT Jian-Li Liu Harbin Institute of Technology 2009 -4 -29 1

Outline u Eccentricity scaled v 2 and incomplete equilibration u Variation of v 2/εwith cross section u Variation of v 2/εwith centrality u Summary 2009 -4 -29 2

Eccentricity scaled v 2 and incomplete equilibration Collisionless limit: Heiselberg & Levy, PRC 59, 2716(1999) Ideal hydrodynamic limit: From collisionless limit to hydrodynamic limit: Bhalerao et al. , PLB 627, 49(2005) work well in 2 -D transport model. 2009 -4 -29 Gombeaud & Ollitrault, PRC 77, 054904(2008) 3

Knudsen coefficient Only longitudinal expansion: (d. N/dy is constant) Time scale of formation of elliptic flow: Bhalerao et al. , PLB 627, 49(2005) 2009 -4 -29 4

AMPT model data Lin et al. , PRC 72, 064901(2005) Differences: 1. cs is not constant from parton to hadron, BUT cs is approximately constant in parton stage 2. d. N/dy is not constant. 3. 3 -D expansion 4. Non-isotropic differential cross section. Molnar & Gyulassy, NPA 697, 459(2002) 2009 -4 -29 5

Relation between isotropic cross section and anisotropic cross section For isotropic cross section: AMPT model: μis turned to fixed total cross section. Transport cross section is related to μ and s. 2009 -4 -29 6

Variation of v 2/εwith cross section for quark σ=3, 6, 10, 14 mb Fitting parameters： Gombeaud et al. 2 -D transport model (2008): 19% 27% Ideal hydrodynamics： Issah et al. , ar. Xiv: nucl-ex/0604011 Initial d. N/dy： final s ： initial d. N/dy，final s ： K 0 is sensitive to parameters used 2009 -4 -29 7

Variation of v 2/εwith cross section for hadron ε，S is calculated for hadron from HIJING Fitting parameters： K 0（c）is much larger than K 0 for quark: 1. Multiplicity difference HIJING hadron initial parton final parton hadron(c) hadron(f) 19% 11% 27% 15% 2. Variation of v 2 (c)/v 2 (quark) from 1. 27 to 1. 1 for cross section from 3 mb to 14 mb. 2009 -4 -29 8

Variation of v 2/εwith cross section for hadron ε，S is calculated for hadron from HIJING hadron Fitting parameters： initial parton final Keeping d. N/dy unchanged and replace parton hadron(c) V 2(f) with V 2 (c): Deviation of elliptic flow from its hadron(f) hydrodynamic limit is almost the same as hadron(c). Keeping elliptic flow unchanged and Replace d. N(f)/dy with d. N(c)/dy: Deviation of elliptic flow from its hydrodynamic limit is almost unchanged. 2009 -4 -29 11% 14% 15% 20% 9

Variation of v 2/εwith centrality for quark 2009 -4 -29 10

Changing the calculation of Knudsen coefficient 2009 -4 -29 11

Changing the calculation of eccentricity consistent with ideal hydrodynamic result Calculate eccentricity for quarks in all rapidity range. 2009 -4 -29 12

Only changing the calculation of eccentricity 2009 -4 -29 13

Possible reasons for changed calculation of Knudsen coefficient 1. Knudsen coefficient at initial stage： 2. “Effective” calculation of Knudsen coefficient defined by Bhalerao et al. : The transverse expansion of system maybe important and is related to the size of system. 2009 -4 -29 14

Variation of v 2/εwith centrality for hadron Original calculation of Knudsen coefficient New calculation of Knudsen coefficient Dependence on cross section： 1. Relative distance between quark is related to cross section. 2. Quarks are coalesced according to their relative cross section 2009 -4 -29 15

Variation of v 2/εwith centrality for hadron Original calculation of Knudsen coefficient New calculation of Knudsen coefficient Dependence on cross section. 2009 -4 -29 16

Summary v 2 /εvariation with cross section for fixed parameter in AMPT model could be described well by the formula suggested Bhalerao et al. The deviation of v 2 /εof quark from its hydrodynamics limit is 19%～ 27% for cross section from 6 mb to 10 mb. v 2 /εvariation with centrality for different cross section and collision energy in AMPT model could not be described by the formula suggested by Bhalerao et al, except the calculation of knudsen coefficient is changed. 2009 -4 -29 17

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