11/23/2009 1 Examine the species and beam-energy dependence of particle spectra using Tsallis...
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Transcript of 11/23/2009 1 Examine the species and beam-energy dependence of particle spectra using Tsallis...
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)
)1/(1])1(
1[)(exp
)exp(
qTTq
T
T
mq
T
mT
mParticle pT spectra:
Exponential Power law
11/23/2009 7
Temperature fluctuation
qT
TT
1
/1
/1/12
22
Wilk and Wlodarzcyk, EPJ40, 299 (2009)Wilk and Wlodarzcyk, PRL84, 2770 (2000)
Reverse legend
11/23/2009 8
Tsallis statistics in Blast-wave model
)1/(1])1(
1[)(exp)exp( qTT
qT
T
mq
T
m
T
m
3
3
1 00
1
2
0 1
0 0
cosh sinh
tanh 0.5,1,2
1( ) exp[ cos( )] , ( ) cosh( )exp[ cosh( )]
2
fo(u p )/T
RT T
TT T fo fo
r r S
d NE e pddp
m pdNrdrm K I
m dm T T
r
R
I z z d K z y z y dy
BGBW:
With Tsallis distribution:
The Blast-wave equation is:
R
qTT
Y
Y
TTT
pymT
qrdrddyym
dmm
dN
0
)1/(1)]}cos()sinh()cosh()cosh([1
1{)cosh(
11/23/2009 9
Fit results in Au+Au collisionsZBT,Yichun Xu, Lijuan Ruan, Gene van Buren, Fuqiang Wang and Zhangbu Xu, Phys. Rev. C 79, 051901 (R) (2009)
11/23/2009 10
Fit strange hadrons only
Strangeness, Au+Au 0-10%:<> = 0.464 +- 0.006 T = 0.150 +- 0.005 q = 1.000 +- 0.002chi^2/nDof = 51/99
Tstrange>Tlight-hadrons
Strangness decouple from the system earlier
All available species
11/23/2009 11
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
11/23/2009 13
J/ suppression at RHIC and SPS
Grandchamp, Rapp, BrownPRL 92, 212301 (2004) nucl-ex/0611020
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!
11/23/2009 14
J/Elliptic flow
Heavy Flavor decay electron
Too early to compare with modelsWon’t have enough statistics before 2011
J/
Ermias T. Atomssa, QM2009
Alan Dion, QM2009
PHENIX Beam Use Request
11/23/2009 15
How about radial flow?
Yifei Zhang, QM2008, STAR, arXiv:nucl-ex/0805.0364 (submitted to PRL)
Sizeable radial flow for heavy flavor decay electrons
11/23/2009 16
J/ radial flow
<> = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 2/nDof = 85.03 / 26
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
Check— Parameter Correlation
11/23/2009 18
<> = 0.0000 +- 0.0000T = 0.1747 +- 0.1644q = 1.0708 +- 0.04352/nDof = 12.83 / 13
<> = 0.0954 +- 0.0828T = 0.1777 +- 0.0328q = 1.0106 +- 0.00222/nDof = 151.53 / 37
11/23/2009 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/ 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