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Tsallis Interperation in Heavy-ion (HI) Physics

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/ y radial flow

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Tsallis Interperation in Heavy-ion (HI) Physics

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  1. 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/y radial flow • Conclusion NanChang, April 19, 2010

  2. 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 NanChang, April 19, 2010 2

  3. Hydrodynamics evolution π, K, p Multi-strange W Hydro parameters: 0 = 0.6 fm/c s0 = 110 fm-3 s0/n0 = 250 Tcrit=Tchem=165 MeV Tdec=100 MeV Ulrich Heinz, arXiv:0901.4355 Multi-strange particle spectra can be well described by the same hydrodynamics parameters as light hadrons in contrast to the Blast-wave results NanChang, April 19, 2010 3

  4. boosted E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993) random Extract thermal temperature Tfo and velocity parameter T Blast-Wave Model • Assumptions: • Local thermal equilibrium  Boltzmann distribution • Longitudinal and transverse expansions (1+2) • Temperature and T are global quantities BGBW: Boltzmann-Gibbs Blast-Wave NanChang, April 19, 2010 4

  5. STAR PRL99 Limitation of the Blast-wave STAR PRC71 (2005) 64902 • Strong assumption on local thermal equilibrium • Arbitrary choice of pT range of the spectra • Non-zero flow velocity <bT>=0.2 in p+p • Lack of non-extensive quantities to describe the evolution from p+p to central A+A collisions • mT spectra in p+p collisions Levy function or mT power-law • mT spectra in A+A collisions Boltzmann or mT exponential AuAu@200GeV pp@200GeV minbias NanChang, April 19, 2010 5

  6. Particle pT spectra: Exponential  Power law 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) NanChang, April 19, 2010

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

  8. 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) NanChang, April 19, 2010 8

  9. Fit strange hadrons only All available species Strangeness, Au+Au 0-10%: <b> = 0.464 +- 0.006 T = 0.150 +- 0.005 q = 1.000 +- 0.002 chi^2/nDof = 51/99 Tstrange>Tlight-hadrons Strangness decouple from the system earlier NanChang, April 19, 2010 9

  10. Centrality dependence for T and <bT> • 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 NanChang, April 19, 2010 10

  11. Beam energy dependence • The radial flow velocity at SPS is smaller than that at RHIC. • Freeze-out temperatures are similar at RHIC and SPS. • 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 NanChang, April 19, 2010 11

  12. How about heavy hadrons? NanChang, April 19, 2010 12

  13. Grandchamp, Rapp, Brown PRL 92, 212301 (2004) nucl-ex/0611020 Puzzle! Regeneration? Test with J/y flow. J/y suppression at RHIC ≈ J/y suppression at SPS (energy differs by ~10 times) J/y suppression at RHIC and SPS • quarkonium – gloden probe of QGP • deconfinement (color screening) • thermometer NanChang, April 19, 2010 13

  14. PHENIX Beam Use Request J/y Elliptic flow J/y Heavy Flavor decay electron Alan Dion, QM2009 Too early to compare with models Won’t have enough statistics before 2011 Ermias T. Atomssa, QM2009 NanChang, April 19, 2010 14

  15. How about radial flow? Sizeable radial flow for heavy flavor decay electrons Yifei Zhang, QM2008, STAR, arXiv:0805.0364 (submitted to PRL) NanChang, April 19, 2010 15

  16. <b> = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 c2/nDof = 85.03 / 26 J/y radial flow J/y radial flow consistent with 0 Inconsistent with regeneration NanChang, April 19, 2010 16

  17. 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/y 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! NanChang, April 19, 2010 17

  18. Back up NanChang, April 19, 2010 18

  19. Check— Parameter Correlation <b> = 0.0954 +- 0.0828 T = 0.1777 +- 0.0328 q = 1.0106 +- 0.0022 c2/nDof = 151.53 / 37 <b> = 0.0000 +- 0.0000 T = 0.1747 +- 0.1644 q = 1.0708 +- 0.0435 c2/nDof = 12.83 / 13 NanChang, April 19, 2010 19

  20. Check—Strangeness and light hadrons NanChang, April 19, 2010 20

  21. Results in p+p collisions NanChang, April 19, 2010 21

  22. Temperature fluctuation Reverse legend Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) 1/14/2010 NanChang, April 19, 2010 22

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