2010/10/1 8 ATHIC2010, Oct 18-20, Wuhan 1 Systematic study of particle spectra in heavy- ion collisions using Tsallis statistics 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
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2010/10/18ATHIC2010, Oct 18-20, Wuhan1 Systematic study of particle spectra in heavy-ion collisions using Tsallis statistics Ming Shao, Zebo Tang, Yi Li,
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2010/10/18 ATHIC2010, Oct 18-20, Wuhan 1
Systematic study of particle spectra in heavy-ion collisions
using Tsallis statistics
Ming Shao, Zebo Tang, Yi Li, Zhangbu XuCPPT/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
2010/10/18 ATHIC2010, Oct 18-20, Wuhan 2
Thermalization and Radial flow in HI
Thermalization in heavy-ion collisions ?- particle ratios agree with thermal prediction
Matter flows in heavy-ion collisions – all particles have the same collective velocity
2
T T
eff fo T
p mass
T T mass
Phys. Rev. Lett. 92 (2004) 182301 STAR whitepaper
2010/10/18 ATHIC2010, Oct 18-20, Wuhan 3
Multi-strange decouple earlier than light hadrons, with less radial flow velocity
Blast-wave analysis
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Hydrodynamics evolution
π, K, p Multi-strange
Multi-strange particle spectra can be well described by the same hydrodynamics parameters as light hadronsin contrast to the Blast-wave results
Assumptions:– Local thermal equilibrium Boltzmann distribution– Longitudinal and transverse expansions (1+2) – 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
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Limitation of the Blast-wave
• Strong assumption on local thermal equilibrium
• Arbitrary choice of pT range of the spectra
• Non-zero 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
pp@200GeV minbias
STAR PRC71 (2005) 64902
AuAu@200GeV
STAR PRL99
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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, PRL84, 2770 (2000) Wilk 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
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Beam energy dependence
12
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
J/ radial flow consistent with 0Inconsistent with regeneration
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Summary
Identified particle spectra from SPS to RHIC have been analyzed with Tsallis statistics in Blast-wave description (light hadrons, multi-strange hadrons, charmonium)
We found in HIC•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 decouplesThank