1. NanChang, April 19, 20101 Tsallis Interperation in Heavy-ion (HI) Physics Ming Shao, Zebo Tang, Yi Li, Zhangbu Xu CPPT/USTC Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results − strange hadrons vs. light hadrons − beam energy dependence − J/  radial flow Conclusion

2. NanChang, April 19, 20102 1/14/20102 Thermalization and Radial flow in HI Matter flows in heavy-ion collisions – all particles have the same collective velocity Multi-strange decouple earlier than light hadrons

3. NanChang, April 19, 20103 1/14/20103 Hydrodynamics evolution π, K, p Multi-strange  Multi-strange particle spectra can be well described by the same hydrodynamics parameters as light hadrons  in contrast to the Blast-wave results Ulrich Heinz, arXiv:0901.4355 Hydro parameters:  0 = 0.6 fm/c s 0 = 110 fm -3 s 0 /n 0 = 250 T crit =T chem =165 MeV T dec =100 MeV

4. NanChang, April 19, 20104 1/14/20104 Blast-Wave Model Assumptions: –Local thermal equilibrium  Boltzmann distribution –Longitudinal and transverse expansions (1+2) –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

5. NanChang, April 19, 20105 1/14/20105 Limitation of the Blast-wave Strong assumption on local thermal equilibrium Arbitrary choice of p T range of the spectra Non-zero 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 pp@200GeV minbias STAR PRC71 (2005) 64902 AuAu@200GeV STAR PRL99

6. NanChang, April 19, 20106 1/14/2010 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, PRL84, 2770 (2000) Wilk and Wlodarzcyk, EPJ40, 299 (2009) Particle p T spectra: Exponential  Power law

7. NanChang, April 19, 20107 1/14/2010 Tsallis statistics in Blast-wave model BGBW: With Tsallis distribution: Tsallis Blast-wave (TBW) equation is:

8. NanChang, April 19, 20108 1/14/20108 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)

9. NanChang, April 19, 20109 1/14/20109 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

10. NanChang, April 19, 201010 1/14/201010 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

11. NanChang, April 19, 201011 Beam energy dependence 1/14/201011 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

12. NanChang, April 19, 201012 1/14/201012 How about heavy hadrons?

13. NanChang, April 19, 201013 1/14/201013 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. NanChang, April 19, 201014 1/14/201014 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. NanChang, April 19, 201015 1/14/201015 How about radial flow? Yifei Zhang, QM2008, STAR, arXiv:0805.0364 (submitted to PRL) Sizeable radial flow for heavy flavor decay electrons

16. NanChang, April 19, 201016 1/14/201016 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. NanChang, April 19, 201017 1/14/201017 Summary Identified particle spectra from SPS to RHIC have been analyzed with Tsallis statistics in Blast-wave description (light hadrons, multi-strange hadrons, charmonium) Partonic phase –Partons achieve thermal equilibrium in central heavy-ion collisions –J/  is not thermalized and disfavors 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 Thank you!

18. NanChang, April 19, 201018 Back up 1/14/201018

19. NanChang, April 19, 201019 Check— Parameter Correlation 1/14/201019 = 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

20. NanChang, April 19, 201020 Check—Strangeness and light hadrons 1/14/201020

21. NanChang, April 19, 201021 Results in p+p collisions 1/14/2010

22. NanChang, April 19, 201022 1/14/201022 Temperature fluctuation Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) Reverse legend