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Mini-jet thermalization and diffusion of transverse correlations in heavy ion collisions

Mini-jet thermalization and diffusion of transverse correlations in heavy ion collisions. Qun Wang ( 王群 ) Univ of Sci & Tech of China ( 中国科技大学 ) With L.G.Pang,X.N.Wang,R.Xu STAR Regional Meeting, Pusan, Korea, May 6-9,2009. What is viscosity related to RHIC.

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Mini-jet thermalization and diffusion of transverse correlations in heavy ion collisions

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  1. Mini-jet thermalization and diffusion of transverse correlations in heavy ion collisions Qun Wang (王群) Univ of Sci & Tech of China (中国科技大学) With L.G.Pang,X.N.Wang,R.Xu STAR Regional Meeting, Pusan, Korea, May 6-9,2009

  2. What is viscosity related to RHIC viscosity = resistance of liquid to shear forces (and hence to flow)

  3. Shear viscosity in ideal gas and liquid ideal gas, high T liquid, low T lower bound by uncertainty principle Danielewicz, Gyulassy, 1985

  4. Ratio of Shear Viscosity to entropy density Lacey et al, PRL98,092301 (2007)

  5. Momentum fluctuation as tool to measure shear viscosity (1) About fluctuation: Schuster’s talk Dunlop’s talk Cylindrical coordinate EM tensor for fluid EM conservation of fluid to equation for fluctuation [Gavin, Abdel-Aziz, PRL 2006] local rest frame

  6. Momentum fluctuation as tool to measure shear viscosity (2) Diffusion equation for momentum density Diffusion equation for momentum density in rapidity and proper time

  7. Momentum fluctuation as tool to measure shear viscosity (3) Correlation of momentum fluctuation Diffusion equation for correlation is broadened by momentum diffusion

  8. Momentum fluctuation as tool to measure shear viscosity (4) Connection to observable • i labels particles from each event • bracketsrepresent the event average Shear viscosity can broaden the rapidity correlations of the momentum current. This broadening can be observed by measuring the transverse momentum covariance as a function of rapidity acceptance.

  9. Momentum fluctuation as tool to measure shear viscosity (5) Rapidity correlations to measure the shear viscosity [Gavin, Abdel-Aziz, PRL 2006]

  10. Azimuthal correlation in transverse momenta Transverse plane can be separated to -bins Focus on two -bins 1 and 2, define correlation function particle numbers in bins 1 and 2 i,j: particles in bins 1 and 2 average is taken over events

  11. Diffusion equation for azimuthal correlationin central collisions Cylindrical coordinates, metrics and velocity Diffusion equation for azimutha correlation central collision

  12. Diffusion equation for azimuthal correlationin central collisions In the co-moving frame without fluid velocity, diffusion equation is in a simple form with solution

  13. Solve diffusion equation in general frame 1. Initial condition given by HIJING 2. Solve fluid equation to determine thermodynamic quantities as input to diffusion equation 3. Average over freeze-out hyper-surface freeze-out energy density

  14. Azimuthal correlation in transverse momentaresult from HIJING

  15. Results for azimuthal correlation (1) Free Gas

  16. Results for azimuthal correlation (2) First order phase transition

  17. Results for azimuthal correlation (3)

  18. Results for azimuthal correlation (4)

  19. Results for azimuthal correlation (5)

  20. Results for azimuthal correlation (6)

  21. Summary and conclusion 1. A diffusion equation for azimuthal correlation for transverse momentum is derived a general Lorentz frame. 2. Mini-jet thermalization is shown in the correlation 3. Azimuthal correaltion as a measure for shear viscosity

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