Transcript Document

Examine the species and beam-energy dependence
of particle spectra using Tsallis Statistics
Li Yi
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
− J/y radial flow
− beam energy dependence
 Conclusion
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Thermalization and Radial flow
From Blast-Wave
Matter flows – all particles have the
same collective velocity:
pT  mass  T
Teff  T fo  mass  T
2
Multi-strange decouple earlier than light hadrons
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Hydrodynamics evolution
Light hadrons
Multi-strange W
Decouple with
pion and proton
Decouple at
chemical freeze-out
Ulrich Heinz, arXiv:0901.4355
Multi-strange particle spectra can be well described by the same
hydrodynamics at the same freeze-out as light hadrons
in contrast to the Blast-wave results
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Blast-Wave Model
Source is assumed to be:
– Local thermal equilibrated  Boltzmann distribution
– Boosted radically
– Temperature and T
are global quantities
boosted
E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993)
d 3N
(u  p  )/T fo
E 3 e
pd  
dp

dN

mT dmT

R
0
  tanh1  r
random
m cosh   p sinh  
T
T
rdrmT K1
I



0
 T
  T


fo
 
fo

r 
 r   S  
R 
  0.5,1,2
Nu Xu
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
• 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
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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, EPJ40, 299 (2009)
Particle pT spectra:
mT
)
T
m
(q  1)mT 1/(q 1)
expq ( T )  [1 
]
T
T
exp(
Exponential  Power law
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Temperature fluctuation
Reverse legend
1/ T
2
 1/ T
1/ T
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2
 1 q
Wilk and Wlodarzcyk, EPJ40, 299 (2009)
Wilk and Wlodarzcyk, PRL84, 2770 (2000)
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Tsallis statistics in Blast-wave model
d3N
(u  p )/T fo
E

e
pd   

dp 3
BGBW:
 mT cosh    pT sinh  
R
dN
  rdrmT K1 
I 0 


0
mT dmT
T
T
fo
fo

 


r
r  S  
R
  tanh 1  r
1
I0 ( z) 
2
2
 exp[ z cos( )]d ,
0
  0.5,1, 2

K1 ( z )   cosh( y ) exp[  z cosh( y )]dy
0
With Tsallis distribution:
exp( 
mT
m
(q  1)mT 1/(q 1)
)  exp q ( T )  [1 
]
T
T
T
The Blast-wave equation is:
Y

dN
q 1
 mT  cosh( y)dy  d  rdr{1 
[mT cosh( y) cosh(  )  pT sinh(  ) cos( )]}1/(q 1)
mT dmT
T
Y

0
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Fit results in Au+Au collisions
ZBT,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
All available species
Strangeness, Au+Au 0-10%:
<> = 0.464 +- 0.006
T = 0.150 +- 0.005
q = 1.000 +- 0.002
chi^2/nDof = 51/99
Tstrange>Tlight-hadrons
Strangness decouple from
the system earlier
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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
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How about heavy hadrons?
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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.
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J/y suppression at RHIC ≈
J/y suppression at SPS
(energy differs by ~10 times)
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J/yElliptic flow
Heavy Flavor decay electron
J/y
PHENIX Beam Use Request
Alan Dion, QM2009
Too early to compare with models
Won’t have enough statistics before 2011
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Ermias T. Atomssa, QM2009
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How about radial flow?
Sizeable radial flow for heavy flavor decay electrons
Yifei Zhang, QM2008, STAR, arXiv:nucl-ex/0805.0364 (submitted to PRL)
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J/y radial flow
<> = 0.06 +- 0.03
T = 0.134 +- 0.006
q =1.0250 +- 0.0014 c2/nDof = 85.03 / 26
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J/y radial flow consistent with 0
Inconsistent with regeneration
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Beam energy dependence
s  17.2GeV
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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Check— Parameter Correlation
<> = 0.0000 +- 0.0000
T
= 0.1747 +- 0.1644
q
= 1.0708 +- 0.0435
2
c /nDof = 12.83 / 13
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<> = 0.0954 +- 0.0828
T
= 0.1777 +- 0.0328
q
= 1.0106 +- 0.0022
c2/nDof = 151.53 / 37
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Check—Strangeness and light hadrons
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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/y 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
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