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Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics

Li Yi. Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics. Zebo Tang , Ming Shao, Zhangbu Xu. Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results strange hadrons vs. light hadrons

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Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics

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

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

  3. Decouple with pion and proton Decouple at chemical freeze-out Hydrodynamics evolution Light hadrons Multi-strange W Ulrich Heinz, arXiv:0901.4355 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

  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 • Source is assumed to be: • Local thermal equilibrated  Boltzmann distribution • Boosted radically • Temperature and T are global quantities Nu Xu BGBW: Boltzmann-Gibbs Blast-Wave

  5. Limitation of the Blast-wave • Strong assumption on local thermal equilibrium • Arbitrary choice of pT range of the spectra • 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

  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, EPJ40, 299 (2009)

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

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

  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. 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

  11. 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

  12. How about heavy hadrons?

  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

  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

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

  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

  17. 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

  18. 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

  19. Check—Strangeness and light hadrons

  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/y 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

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