NanChang, April 19, 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
NanChang, April 19, /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
NanChang, April 19, /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: 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
NanChang, April 19, /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
NanChang, April 19, /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 minbias STAR PRC71 (2005) STAR PRL99
NanChang, April 19, /14/2010 Non-extensive Tsallis statistics C. Tsallis, H. Stat. Phys. 52, 479 (1988) Wilk and Wlodarzcyk, PRL84, 2770 (2000) Wilk and Wlodarzcyk, EPJ40, 299 (2009) Particle p T spectra: Exponential Power law
NanChang, April 19, /14/2010 Tsallis statistics in Blast-wave model BGBW: With Tsallis distribution: Tsallis Blast-wave (TBW) equation is:
NanChang, April 19, /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, (R) (2009)
NanChang, April 19, /14/20109 Fit strange hadrons only Strangeness, Au+Au 0-10%: = T = q = chi^2/nDof = 51/99 T strange >T light-hadrons Strangness decouple from the system earlier All available species
NanChang, April 19, /14/ 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
NanChang, April 19, Beam energy dependence 1/14/ 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
NanChang, April 19, /14/ How about heavy hadrons?
NanChang, April 19, /14/ J/ suppression at RHIC and SPS Grandchamp, Rapp, Brown PRL 92, (2004) nucl-ex/ 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!
NanChang, April 19, /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
NanChang, April 19, /14/ How about radial flow? Yifei Zhang, QM2008, STAR, arXiv: (submitted to PRL) Sizeable radial flow for heavy flavor decay electrons
NanChang, April 19, /14/ J/ radial flow = T = q = 2 /nDof = / 26 J/ radial flow consistent with 0 Inconsistent with regeneration
NanChang, April 19, /14/ 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!
NanChang, April 19, Back up 1/14/201018
NanChang, April 19, Check— Parameter Correlation 1/14/ = T = q = 2 /nDof = / 13 = T = q = 2 /nDof = / 37
NanChang, April 19, Check—Strangeness and light hadrons 1/14/201020
NanChang, April 19, Results in p+p collisions 1/14/2010
NanChang, April 19, /14/ Temperature fluctuation Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) Reverse legend