1. 11/23/2009 1 Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics Zebo Tang, Ming Shao, Zhangbu Xu Li Yi Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results − strange hadrons vs. light hadrons − J/  radial flow − beam energy dependence Conclusion

2. 11/23/2009 2 Thermalization and Radial flow Matter flows – all particles have the same collective velocity: Multi-strange decouple earlier than light hadrons From Blast-Wave

3. 11/23/2009 3 Decouple at chemical freeze-out Decouple with pion and proton Hydrodynamics evolution Light hadrons Multi-strange  Multi-strange particle spectra can be well described by the same hydrodynamics at the same freeze-out as light hadrons  in contrast to the Blast-wave results Ulrich Heinz, arXiv:0901.4355

4. 11/23/2009 4 Blast-Wave Model Source is assumed to be: –Local thermal equilibrated  Boltzmann distribution –Boosted radically –Temperature and  T  are global quantities random boosted E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993) Extract thermal temperature T fo and velocity parameter  T  BGBW: Boltzmann-Gibbs Blast-Wave Nu Xu

5. 11/23/2009 5 Limitation of the Blast-wave Strong assumption on local thermal equilibrium Arbitrary choice of p T range of the spectra Flow velocity =0.2 in p+p Lack of non-extensive quantities to describe the evolution from p+p to central A+A collisions –m T spectra in p+p collisions Levy function or m T power-law –m T spectra in A+A collisions Boltzmann or m T exponential

6. 11/23/2009 6 Non-extensive Tsallis statistics C. Tsallis, H. Stat. Phys. 52, 479 (1988) http://www.cscs.umich.edu/~crshalizi/notabene/tsallis.html http://tsallis.cat.cbpf.br/biblio.htm Wilk and Wlodarzcyk, EPJ40, 299 (2009) Particle p T spectra: Exponential  Power law

7. 11/23/2009 7 Temperature fluctuation Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) Reverse legend

8. 11/23/2009 8 Tsallis statistics in Blast-wave model BGBW: With Tsallis distribution: The Blast-wave equation is:

9. 11/23/2009 9 Fit results in Au+Au collisions ZBT,Yichun Xu, Lijuan Ruan, Gene van Buren, Fuqiang Wang and Zhangbu Xu, Phys. Rev. C 79, 051901 (R) (2009)

10. 11/23/2009 10 Fit strange hadrons only Strangeness, Au+Au 0-10%: = 0.464 +- 0.006 T = 0.150 +- 0.005 q = 1.000 +- 0.002 chi^2/nDof = 51/99 T strange >T light-hadrons Strangness decouple from the system earlier All available species

11. 11/23/2009 11 Centrality dependence for T and <    Multi-strange hadrons decouple earlier Hadron rescattering at hadronic phase doesn’t produce a collective radial flow, instead, it drives the system off equilibrium Partons achieve thermal equilibrium in central collisions

12. 11/23/2009 12 How about heavy hadrons?

13. 11/23/2009 13 J/  suppression at RHIC and SPS Grandchamp, Rapp, Brown PRL 92, 212301 (2004) nucl-ex/0611020 Regeneration? Test with J/  flow. quarkonium – gloden probe of QGP deconfinement (color screening) thermometer J/  suppression at RHIC ≈ J/  suppression at SPS (energy differs by ~10 times) Puzzle!

14. 11/23/2009 14 J/  Elliptic flow Heavy Flavor decay electron Too early to compare with models Won’t have enough statistics before 2011 J/  Ermias T. Atomssa, QM2009 Alan Dion, QM2009 PHENIX Beam Use Request

15. 11/23/2009 15 How about radial flow? Yifei Zhang, QM2008, STAR, arXiv:nucl-ex/0805.0364 (submitted to PRL) Sizeable radial flow for heavy flavor decay electrons

16. 11/23/2009 16 J/  radial flow = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014  2 /nDof = 85.03 / 26 J/  radial flow consistent with 0 Inconsistent with regeneration

17. Beam energy dependence 11/23/2009 17 1.The radial flow velocity at SPS is smaller than that at RHIC. 2.Freeze-out temperatures are similar at RHIC and SPS. 3.The non-equilibrium parameter (q-1) is small in central nucleus-nucleus collisions at RHIC and SPS except a larger (q -1) value for non-strange hadrons at RHIC energy

18. Check— Parameter Correlation 11/23/2009 18 = 0.0000 +- 0.0000 T = 0.1747 +- 0.1644 q = 1.0708 +- 0.0435  2 /nDof = 12.83 / 13 = 0.0954 +- 0.0828 T = 0.1777 +- 0.0328 q = 1.0106 +- 0.0022  2 /nDof = 151.53 / 37

19. Check—Strangeness and light hadrons 11/23/2009 19

20. 11/23/2009 20 Summary Identified particle spectra from SPS to RHIC has been analyzed with Tsallis statistics in Blast-wave description (light hadrons, multi-strange hadrons, charmonium) Partonic phase –Partons achieve thermal quilibrium in central heavy-ion collisions –J/  are not thermalized and disfavor regeneration Multi-strange hadrons decouple earlier Hadronic phase –Hadronic rescattering doesn’t produce collective radial flow –It drives the system off equilibrium –Radial flow reflects that when the multi-strange decouples