1. Elliptic flow of thermal photons in Au+Au collisions at 200GeV QNP2009 Beijing, Sep 21 - 26, 2009 F.M. Liu Central China Normal University, China T. Hirano University of Tokyo, Japan K. Werner University of Nantes, France Y. Zhu Central China Normal University, China

2. 2 Outline Motivations Calculation approach Results Conclusion

3. 3 Motivations The properties of the hot dense matter created in heavy ion collision are of great interest, especially the critical behaviors. As penetrating probes, thermal photons can provide the inner information of the plasma, which is a useful compensation to the signals of hadrons emitted from the surface of the plasma. Questions: What can we learn from direct photon signals? How is thermal photon signal, i.e. the elliptic flow, related to the system evolution? …

4. 4 Calculation approach A precise calculation of direct photon production requires careful treatments on All sources of direct photons: from primordial scatterings at early stage, thermal photons, jet photon conversion, fragmentation contribution, … The space-time evolution of the created hot dense matter  distributions of thermal partons  thermal photons, low pt hadrons The propagation of jets in plasma (energy loss)  distribution of hard partons  high pt photons and hadrons

5. 5 thermal photon production Thermal parton interactions are considered in emission rate: In the local rest frame, photons are emitted from the thermal bath isotropically. Thermal photons’ v2 is caused by the Lorentz boost and accumulated with the space-time integration. Both the strength and the asymmetry of the transverse flow are important.

6. 6 the evolution of the matter Initial condition: thermalized QCD matter at Freeze-out: Evolution: 3D ideal hydrodynamic equation described with 3+1D ideal hydrodynamics EoS: 1st order phase transition at QGP phase: 3 flavor free Q & G gas HG phase: hadronic gas PCE

7. 7 Initial conditions at Flow velocity: zero Energy density: (two options) Parameterized based on Glauber model—a plateau is assumed. Hirano et al. Phys. Rev. C77:044909, 2008 EPOS model: based on string overlapping. K.Werner@SQM09 Uniform distribution is assumed along longitudinal direction in 2+1D hydrodynamics Parameters constrained with PHOBOS data Tested with hadrons’ yields, spectra, v2 and particles correlation

8. 8 Time evolution of the plasma Energy-weighted Space-averaged Energy density gets weaker with time. Transverse flow gets stronger with time. The asymmetry increases with eccentricity.

9. 9 FML, T.Hirano, K.Werner, Y. Zhu Phys. Rev. C 79, (2009) 014905; J. Phys. G 36 (2009) 064072. Results: Pt spectra of direct photons Direct photon production from AuAu collisions at top RHIC energy is well explained in a large pt range at all centralities. The effect from jet quenching is discussed.

10. 10 pt dependence of thermal photon v2 Elliptic flow of thermal photons decreases at high pt due to the abundant emission at early time. FML, T.Hirano, K.Werner, Y. Zhu, Phys. Rev. C80,034905 (2009).

11. 11 Centrality dependence of pt-int. v2 Maximum appears at 40-50% centrality. Why? Note: The maximum of measured hadronic v2 also appears at this centrality, but viscosity is needed to explain it. Both strength and asymmetry of transverse flow are important. Thermal photons dominant the low pt contribution and become the main part in the pt-integrated v2 of direct photons. When compared with measurements, one should be careful with minimum pt.

12. 12 Rapidity dependence The rapidity distribution can not identify different initial conditions; But the elliptic flow of thermal photons “remembers” the initial conditions.

13. 13 Thermal photons from eta_s source Parameterized initial condition EPOS initial condition

14. 14 Conclusion Ideal hydro model can reproduce the measured pt spectra of direct photons at different centrality with the four sources we considered. Thermal photons’ v2 decreases at higher pt due to more fraction from early emission. We predict thermal photons’ v2 reaches maximum at 40-50% centrality, due to the interplay between the strength and asymmetry of the transverse flow. Contrary to hadronic v2, no need of viscosity here. Thermal photons dominant the low pt contribution and become the main part in the pt-integrated v2 of direct photons. Similar to hadronic signal, the rapidity distribution of thermal photons’ v2 can reveal the initial longitudinal energy/entropy distribution.

15. 15 Thank you!

16. 16 Initial condition ： Glauber model Parameterized rapidity distribution in pp collisions Energy density or entropy distribution in the space:

17. 17 EPOS initial condition Strings are constructed randomly in NN collisions. String segments overlap in the space and form the core and corona region.

18. 18 thermal photons v2 time evolution Fraction emitted at earlier time Increases with pt. Elliptic flow of thermal photons increases with time.

19. 19 Dependence of EoS? Elliptic flow is more sensitive to EoS than pt spectrum! Various input of EoS

20. 20 QGP phase and HG phase V2 from hadronic phase is much bigger than from QGP phase. V2 can carry different information than pt spectrum.

21. 21 Pt spectrum from pp collisions PRL 98, 012002 (2007) A good test for contributions from leading order + fragmentation without Eloss in AA collisions.

22. 22 Isosping mixture and nuclear shadowing: R AA suppression from initial effect The dominant contribution at high pt is the LO contribution from NN collisions: The isospin mixture and nuclear shadowing reduce Raa at high pt. This is the initial effect, not related to QGP formation.

23. 23 Distribution of hard partons MRST 2001 LO pDIS and EKS98 nuclear modification are employed Jet phase space distribution at τ=0: at τ>0:

24. 24 Why jets lose energy

25. 25 Fix D with pi0 suppression From pp collisions: From AA collisions, parton energy loss is considered via modified fragmentation function Factorization scale and renormalization scale to be X.N.Wang’s formula

26. 26 Parton Energy Loss in a Plasma Energy loss of parton i=q, g, Energy loss per unit distance, i,e, with BDMPS D: free parameter Every factor depends on the location of jet in plasma, i.e., f QGP : fraction of QGP at a given point

27. 27 Fix D with pi0 suppression A common D=1.5 for various Centralities!