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Elliptic flow and incomplete equilibration in AMPT

Elliptic flow and incomplete equilibration in AMPT. Jian-Li Liu Harbin Institute of Technology. Outline. Eccentricity scaled v 2 and incomplete equilibration Variation of v 2 / ε with cross section Variation of v 2 / ε with centrality Summary.

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Elliptic flow and incomplete equilibration in AMPT

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

  2. Outline • Eccentricity scaled v2 and incomplete equilibration • Variation of v2/εwith cross section • Variation of v2/εwith centrality • Summary

  3. Eccentricity scaled v2 and incomplete equilibration Collisionless limit: Heiselberg & Levy, PRC59, 2716(1999) Ideal hydrodynamic limit: From collisionless limit to hydrodynamic limit: Bhalerao et al., PLB627, 49(2005) work well in 2-D transport model.Gombeaud & Ollitrault, PRC77, 054904(2008)

  4. Knudsen coefficient Only longitudinal expansion: (dN/dy is constant) Time scale of formation of elliptic flow: Bhalerao et al., PLB627, 49(2005)

  5. AMPT model data Lin et al., PRC72, 064901(2005) • Differences: • cs is not constant from parton to hadron, BUT cs is • approximately constant in parton stage • 2. dN/dy is not constant. • 3. 3-D expansion • 4. Non-isotropic differential cross section. Molnar & Gyulassy, NPA697, 459(2002)

  6. 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.

  7. Variation of v2/εwith cross section for quark σ=3,6,10,14mb Fitting parameters： 19% Gombeaud et al. 2-D transport model (2008): 27% Ideal hydrodynamics： Issah et al., arXiv:nucl-ex/0604011 Initial dN/dy： final s ： initial dN/dy，final s ： K0 is sensitive to parameters used

  8. Variation of v2/εwith cross section for hadron ε，S is calculated for hadron from HIJING HIJING hadron Fitting parameters： initial parton final parton • K0（c）is much larger than • K0 for quark: • Multiplicity difference • 2. Variation of v2 (c)/v2 (quark) from • 1.27 to 1.1 for cross section from • 3mb to 14mb. hadron(c) hadron(f) 19% 11% 27% 15%

  9. Variation of v2/εwith cross section for hadron ε，S is calculated for hadron from HIJING HIJING hadron Fitting parameters： initial parton final parton Keeping dN/dy unchanged and replace V2(f) with V2 (c): Deviation of elliptic flow from its hydrodynamic limit is almost the same as hadron(c). Keeping elliptic flow unchanged and Replace dN(f)/dy with dN(c)/dy: Deviation of elliptic flow from its hydrodynamic limit is almost unchanged. hadron(c) hadron(f) 14% 11% 20% 15%

  10. Variation of v2/εwith centrality for quark

  11. Changing the calculation of Knudsen coefficient

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

  13. Only changing the calculation of eccentricity

  14. 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.

  15. Variation of v2/εwith centrality for hadron Original calculation of Knudsen coefficient New calculation of Knudsen coefficient • Dependence on cross section： • Relative distance between quark • is related to cross section. • Quarks are coalesced according • to their relative cross section

  16. Variation of v2/εwith centrality for hadron Original calculation of Knudsen coefficient New calculation of Knudsen coefficient Dependence on cross section.

  17. Summary v2 /εvariation with cross section for fixed parameter in AMPT model could be described well by the formula suggested Bhalerao et al. The deviation of v2 /εof quark from its hydrodynamics limit is 19%～27% for cross section from 6mb to 10mb. v2 /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.

  18. Thanks!

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