11/23/200 9 1 Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics Zebo Tang, Ming Shao, Zhangbu Xu Li Yi Introduction & Motivation Why and how to implement Tsallis statistics in Blast- Wave framework Results − strange hadrons vs. light hadrons − J/radial flow − beam energy dependence Conclusion
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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 - PowerPoint PPT Presentation
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11/23/2009 1
Examine the species and beam-energy dependenceof particle spectra using Tsallis Statistics
Zebo Tang, Ming Shao, Zhangbu Xu
Li Yi
Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results
− strange hadrons vs. light hadrons− J/ radial flow− beam energy dependence
Conclusion
11/23/2009 2
Thermalization and Radial flow
Matter flows – all particles have the same collective velocity:
2
T T
eff fo T
p mass
T T mass
Multi-strange decouple earlier than light hadrons
From Blast-Wave
11/23/2009 3
Decouple at chemical freeze-out
Decouple withpion and proton
Hydrodynamics evolution
Light hadrons Multi-strange
Multi-strange particle spectra can be well described by the same hydrodynamics at the same freeze-out as light hadronsin contrast to the Blast-wave results
Ulrich Heinz, arXiv:0901.4355
11/23/2009 4
Blast-Wave Model
Source is assumed to be:– Local thermal equilibrated Boltzmann distribution– Boosted radically
– Temperature and T are global quantities
random
boostedE.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993)
Ed3N
dp3 e (u p )/T fo p
d
dN
mTdmT rdrmTK1
mT coshTfo
0
R I0pT sinhTfo
tanh 1r r Sr
R
0.5,1,2
Extract thermal temperature Tfo and velocity parameter T
BGBW: Boltzmann-Gibbs Blast-Wave
Nu Xu
11/23/2009 5
Limitation of the Blast-wave
• Strong assumption on local thermal equilibrium
• Arbitrary choice of pT range of the spectra
• Flow velocity <T>=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
11/23/2009 6
Non-extensive Tsallis statistics
C. Tsallis, H. Stat. Phys. 52, 479 (1988)http://www.cscs.umich.edu/~crshalizi/notabene/tsallis.htmlhttp://tsallis.cat.cbpf.br/biblio.htmWilk and Wlodarzcyk, EPJ40, 299 (2009)
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
J/ radial flow consistent with 0Inconsistent with regeneration
Beam energy dependence
11/23/2009 17
GeVs 2.17
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
• Partonic phase– Partons achieve thermal quilibrium in central heavy-ion collisions– J/ 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