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/ y radial flow Conclusion ATHIC2010, Oct 18-20, Wuhan 2010/10/18 1

Thermalization and Radial flow in HI

STAR whitepaper Phys. Rev. Lett.

92

(2004) 182301 Thermalization in heavy-ion collisions ?

－ particle ratios agree with thermal prediction Matter flows in heavy-ion collisions – all particles have the same collective velocity

p T



mass

 

T eff



T fo



mass



T



T

2 2010/10/18 ATHIC2010, Oct 18-20, Wuhan 2

Blast-wave analysis Multi-strange decouple earlier than light hadrons, with less radial flow velocity

2010/10/18 ATHIC2010, Oct 18-20, Wuhan 3

Hydrodynamics evolution π, K, p Multi-strange

W 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 Ulrich Heinz, arXiv:0901.4355

Multi-strange particle spectra can be well described by the same hydrodynamics parameters as light hadrons



in contrast to the Blast-wave results

2010/10/18 ATHIC2010, Oct 18-20, Wuhan



Blast-Wave Model

Assumptions: – Local thermal equilibrium  Boltzmann distribution – Longitudinal and transverse expansions (1+2) – Temperature and  

T

 are global quantities

E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993) E d

3

N dp

3

dN m T dm T

   

e



(u



p



)/T fo p d

   0

R rdrm T K

1   

m T

 cosh 

T fo

  

I

0   

p T

sinh

T fo

     tanh  1 

r



r

 

S



r R

     0.5,1,2 random boosted Extract thermal temperature

T fo

and velocity parameter  

T



BGBW: Boltzmann-Gibbs Blast-Wave

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Limitation of the Blast-wave

• Strong assumption on local thermal equilibrium • Arbitrary choice of p T the spectra range of • 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 – 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 STAR PRC71 (2005) 64902 AuAu@200GeV pp@200GeV minbias STAR PRL99 2010/10/18 ATHIC2010, Oct 18-20, Wuhan

2010/10/18

Non-extensive Tsallis statistics

C. Tsallis, H. Stat. Phys. 52, 479 (1988) http://www.cscs.umich.edu/~crshalizi/notabene/tsallis.html

http://tsallis.cat.cbpf.br/biblio.htm

Wilk and Wlodarzcyk, PRL84, 2770 (2000) Wilk and Wlodarzcyk, EPJ40, 299 (2009) Particle p T exp( 

m T

)

T

spectra:  exp

q

( 

m T T

)  [ 1  (

q

 1 )

m T T

]  1 /(

q

 1 ) Exponential  Power law 1 /

T

2  1 /

T

2 1 /

T

2 

q

 1 ATHIC2010, Oct 18-20, Wuhan 7

Tsallis statistics in Blast-wave model

BGBW:

E dp

3

dN m dm T T

  

e



(u p )/T fo pd

    0

R rdrm K T

1  

m T

 cosh   

I T fo

  tanh  1 

r



r

 

S r

  

p T

sinh   

T fo

  0.5,1, 2

I

0  1 2  2  0  

d

 , ( )   0  

z

With Tsallis distribution: exp( 

m T

)  exp

q

( 

T

Tsallis Blast-wave (TBW) equation is:

m T T

)  [ 1  (

q

 1 )

m T T

]  1 /(

q

 1 )

dN m T dm T



m T

 

Y



Y

cosh(

y

)

dy

    

d

 0 

R rdr

{ 1 

q T

 1 [

m T

cosh(

y

) cosh(  ) 

p T

sinh(  ) cos(  )]}  1 /(

q

 1 ) 2010/10/18 ATHIC2010, Oct 18-20, Wuhan 8

Fit results in Au+Au collisions

Phys. Rev. C 79, 051901 (R) (2009) 2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Fit strange hadrons only All available species

2010/10/18

Strangeness, Au+Au 0-10%: <



> = 0.464 +- 0.006

T = 0.150 +- 0.005

q = 1.000 +- 0.002

chi^2/nDof = 51/99 T strange >T light-hadrons Strangness decouple from the system earlier

ATHIC2010, Oct 18-20, Wuhan

Centrality dependence for T and <

 T >  

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

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Beam energy dependence

s

 17 .

2

GeV

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 2010/10/18 ATHIC2010, Oct 18-20, Wuhan

How about heavy hadrons?

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

J/

y

suppression at RHIC and SPS

• •

quarkonium – gloden probe of QGP deconfinement (color screening) thermometer Puzzle!

Grandchamp, Rapp, Brown PRL 92, 212301 (2004) nucl-ex/0611020 Regeneration?

Test with J/ y flow.

2010/10/18

J/

y

J/

y

suppression at RHIC ≈ suppression at SPS (energy differs by ~10 times)

ATHIC2010, Oct 18-20, Wuhan

J/

y

Elliptic flow J/

y

Heavy Flavor decay electron

Alan Dion, QM2009 Too early to compare with models Won’t have enough statistics before 2011 2010/10/18 ATHIC2010, Oct 18-20, Wuhan Ermias T. Atomssa, QM2009

How about radial flow?

Sizeable radial flow for heavy flavor decay electrons

Yifei Zhang, QM2008, STAR, arXiv:0805.0364

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

J/

y

radial flow

<  > = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 c 2 /nDof = 85.03 / 26 2010/10/18 J/ y radial flow consistent with 0 Inconsistent with regeneration ATHIC2010, Oct 18-20, Wuhan

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/ y 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!

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Back up

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Check— Parameter Correlation

<  > = 0.0000 +- 0.0000

T = 0.1747 +- 0.1644

q = 1.0708 +- 0.0435

c 2 /nDof = 12.83 / 13 2010/10/18 ATHIC2010, Oct 18-20, Wuhan <  > = 0.0954 +- 0.0828

T = 0.1777 +- 0.0328

q = 1.0106 +- 0.0022

c 2 /nDof = 151.53 / 37

Check—Strangeness and light hadrons

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Results in p+p collisions

2010/10/18 ATHIC2010, Oct 18-20, Wuhan

Temperature fluctuation

2010/10/18

Reverse legend

1 /

T

2  1 /

T

2 1 /

T

2 

q

 1 Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) ATHIC2010, Oct 18-20, Wuhan

2010/10/18 PHENIX Beam Use Request ATHIC2010, Oct 18-20, Wuhan 24