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Tsallis Fit to RHIC Data

Ming Shao CPST/USTC with Zhangbu Xu, Zebo Tang, Li Yi, Lijuan ruan, and more. Tsallis Fit to RHIC Data. Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results Flavor dependence High pT Conclusion. Thermalization and Radial flow in HI.

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Tsallis Fit to RHIC Data

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  1. Ming Shao CPST/USTC with Zhangbu Xu, Zebo Tang, Li Yi, Lijuan ruan, and more Tsallis Fit to RHIC Data • Introduction & Motivation • Why and how to implement Tsallis statistics in Blast-Wave framework • Results • Flavor dependence • High pT • Conclusion STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

  2. Thermalization and Radial flow in HI STAR whitepaper Phys. Rev. Lett. 92 (2004) 182301 Thermalization in heavy-ion collisions ? －particle ratios agree with thermal prediction Matter flows in heavy-ion collisions – all particles have the same collective velocity 14届全国核物理大会，合肥

  3. Blast-wave analysis Multi-strange decouple earlier than light hadrons, with less radial flow velocity 14届全国核物理大会，合肥

  4. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 4

  5. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 5

  6. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 6

  7. Particle pT spectra: Exponential  Power law Non-extensive Tsallis statistics C. Tsallis, H. Stat. Phys. 52, 479 (1988) Wilk and Wlodarzcyk, PRL84, 2770 (2000) ; Wilk and Wlodarzcyk, EPJ40, 299 (2009) Tsallis Entropy • Why Tsallis statistics? • Memory effect • Long range correlation (small size) • Intrinsic fluctuation • Limited phase space STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

  8. Tsallis statistics in Blast-wave model BGBW: With Tsallis distribution: Tsallis Blast-wave (TBW) equation is: STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

  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) STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 9

  10. Results in p+p collisions STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 10

  11. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 11

  12. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 13

  14. J/y radial flow J/y radial flow consistent with 0, inconsistent with regeneration AuAu: β=0, T=0.2+/-0.4, q-1=0.06+/-0.18 CuCu: β=0, T=0.0+/-0.4, q-1=1.113+/-0.006 pp: β=0, T=0.17+/-0.17, q-1=1.07+/-0.05 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 14

  15. Tsallis fit to high-pT corona (pp) core STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

  16. RAA & v2 1) New extension to v2 still provide high quality fits – indicating bulk as a thermodynamic state. 2) Non-equilibrated component in the core produces a power-law tail in spectra and high v2 at the intermediate pT. 3) The baryon and meson yields are grouped in p+p. 4) 2)+3) together bring down the bulk v2, produce the baryon enhancement and the NCQ scaling at the intermediate pT. 5) The medium quenches the jet (to fpp = 0.40), resulting in a finite v2 emission (9.4%). 6) Data points at low pT dominates the fit 2. STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

  17. Summary • Identified particle spectra at RHIC have been analyzed with Tsallis statistics in Blast-wave description to high pT (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 • Hadronic phase • Multi-strange hadrons decouple earlier • Hadronic rescattering doesn’t produce collective radial flow, but drives the system off equilibrium • Radial flow reflects that when the multi-strange decouples • Unified macroscopic description of hadron spectra/flow to high pT • Core and corona component • Statistical originated NCQ scaling on RAA & v2 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 17

  18. Thank you! STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 19

  20. Check—Strangeness and light hadrons STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 20

  21. Temperature fluctuation Reverse legend Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) 1/14/2010 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 21

  22. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 22

  23. How about radial flow? Sizeable radial flow for heavy flavor decay electrons Yifei Zhang, QM2008, STAR, arXiv:0805.0364 (submitted to PRL) STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 23

  24. 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 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 24

  25. <b> = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 c2/nDof = 85.03 / 26 J/y radial flow STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 25

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