1. Mass ordering of differential elliptic flow and its violation for  mesons Tetsufumi Hirano Dept. of Physics, The Univ. of Tokyo Matsumoto, Feb. 10-11, 2007 Collaborators: U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara

2. Outline “ Dissipative ” effects on final p T spectra and elliptic flow Mass ordering of v 2 (p T ) and its violation for  mesons Nuclear modification factor for  mesons

3. Motivation To understand the QGP in H.I.C., need to understand the hadronic stage since Indispensable to disentangle these effects for understanding unknowns.

4. How Large Hadronic Rescattering? Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. Hydro Model: QGP Fluid + Hadronic Fluid + Glauber I.C. Comparison  Try to draw information on hadron gas Key technique in hydro: Partial chemical equilibrium in hadron phasePartial chemical equilibrium in hadron phase Particle ratio fixed at T chParticle ratio fixed at T ch  Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06) TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

5. Hydro ~ Hydro+Cascade for Protons T th ~ 100 MeVT th ~ 100 MeV Shape of spectrum changes due to radial flow rather than hadronic dissipation forShape of spectrum changes due to radial flow rather than hadronic dissipation forprotons. radial flow

6. Opposite Behaviors for Pions Softer: Hadronic Fluid (pdV work) Harder: Hadronic Gas (Viscous pressure) Green line: Teaney(’03) Caveat: Transverse expansion Non-scaling solution

7. Source Function from 3D Hydro + Cascade Blink: Ideal Hydro, Kolb and Heinz (2003) Caveat: No resonance decays in ideal hydro Chem.eq. is assumed in ideal hydro. How much the source function differs from ideal hydro in Configuration space?

8. Hadronic Dissipation Suppresses Differential Elliptic Flow Difference comes from dissipation only in the hadron phase Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and M.Gyulassy (’06)) Relevant parameter:  s Relevant parameter:  s  Teaney(’03) Teaney(’03) Dissipative effect is not soDissipative effect is not so large due to small expansion rate (1/tau ~ 0.05-0.1 fm -1 )

9. v 2 (  ) from QGP Hydro + Hadronic Cascade Suppression due to hadronic dissipation

10. Excitation Function of v2 Hadronic Dissipation is huge at SPS.is huge at SPS. still affects v 2 at RHIC.still affects v 2 at RHIC. is almost negligible at LHC.is almost negligible at LHC.

11. Mass Ordering of Differential Elliptic Flow and Its Violation for  mesons

12. p T spectra for pi, K, and p Reasonable reproduction of yields and spectra in low p T region  Non trivial!!!

13. v 2 (p T ) for pi, K, and p OK! Due to fluctuation of geometry

14. Origin of Mass Ordering Mass ordering behavior comes from hadronic rescattering.  Not a direct signal of “perfect fluid QGP”

15. What happens to strangeness sector?

16. Additive Quark Model in Transport Code (JAM/RQMD/UrQMD) For cross sections without exp. data, Expected to be very smaller for phi, Omega, etc.

17. Distribution of Freeze-Out Time

18.  -meson case in p T < 1 GeV/c Just after hadronization Final results T = T sw = 169 MeV

19. p T spectra for  mesons It may be dangerous to fit spectra in the whole p T region to obtain freezeout temperature.  p T ~< 1.5 GeV/c ?

20. Nuclear Modification Factor Don’t ask me why K=4.5 for phi mesons! Non-trivial R AA for  mesons

21. Summary Hadronic rescattering effects Change of spectral shape Suppression of v 2 Reproduction of v 2 (p T ) Origin of mass ordering of v 2 (p T ) Violation of mass ordering for phi mesons Non-trivial behavior of R AA for phi mesons