NanChang, April 19, 2010 1

Tsallis Interperation in Heavy-ion (HI) Physics

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

NanChang, April 19, 2010 21/14/2010 2

Thermalization and Radial flow in HI

Matter flows in heavy-ion collisions – 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

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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

Ulrich Heinz, arXiv:0901.4355

Hydro parameters:0 = 0.6 fm/c s0 = 110 fm-3 s0/n0 = 250 Tcrit=Tchem=165 MeV Tdec=100 MeV

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Blast-Wave Model

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)

)1/(1])1(

1[)(exp

)exp(

qTTq

T

T

mq

T

mT

mParticle pT spectra:

Exponential Power law

1/1

/1/12

22

qT

TT

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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:

Tsallis Blast-wave (TBW) equation is:

R

qTT

Y

Y

TTT

pymT

qrdrddyym

dmm

dN

0

)1/(1)]}cos()sinh()cosh()cosh([1

1{)cosh(

NanChang, April 19, 2010 81/14/2010 8

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)

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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

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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, 2010 11

Beam energy dependence

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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

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How about heavy hadrons?

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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!

NanChang, April 19, 2010 141/14/2010 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

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How about radial flow?

Yifei Zhang, QM2008, STAR, arXiv:0805.0364 (submitted to PRL)

Sizeable radial flow for heavy flavor decay electrons

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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

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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)

• 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, 2010 18

Back up

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NanChang, April 19, 2010 19

Check— Parameter Correlation

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<> = 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

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Check—Strangeness and light hadrons

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Results in p+p collisions

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Temperature fluctuation

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22

qT

TT

Wilk and Wlodarzcyk, EPJ40, 299 (2009)Wilk and Wlodarzcyk, PRL84, 2770 (2000)

Reverse legend