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STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1 Tsallis Fit to RHIC Data Ming Shao CPST/USTC with Zhangbu Xu, Zebo Tang, Li Yi, Lijuan ruan, and more Introduction & Motivation Why and how to implement Tsallis statistics in Blast- Wave framework Results Flavor dependence High pT Conclusion 22/6/27

Tsallis Fit to RHIC Data

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Ming Shao CPST/USTC with Zhangbu Xu, Zebo Tang, Li Yi, Lijuan ruan, and more. Tsallis Fit to RHIC Data. Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results Flavor dependence High pT Conclusion. Thermalization and Radial flow in HI. - PowerPoint PPT Presentation

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Page 1: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1

Tsallis Fit to RHIC DataMing ShaoCPST/USTC

with Zhangbu Xu, Zebo Tang, Li Yi, Lijuan ruan, and more

Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results

− Flavor dependence− High pT

Conclusion

23/4/19

Page 2: Tsallis Fit to RHIC Data

2010/10/18 14 届全国核物理大会,合肥 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

Page 3: Tsallis Fit to RHIC Data

2010/10/18 14 届全国核物理大会,合肥 3

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

Blast-wave analysis

Page 4: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 423/4/19 4

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

Page 5: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 523/4/19 5

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

Page 6: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 623/4/19 6

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

Page 7: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 723/4/19

Non-extensive Tsallis statistics

C. Tsallis, H. Stat. Phys. 52, 479 (1988)Wilk 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

Tsallis Entropy

Why Tsallis statistics?

Memory effect

Long range correlation (small size)

Intrinsic fluctuation

Limited phase space

Page 8: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 823/4/19

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(

Page 9: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 923/4/19 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)

Page 10: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1010

Results in p+p collisions

23/4/19

Page 11: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1123/4/19 11

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

Page 12: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1223/4/19 12

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

Page 13: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1323/4/19 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!

Page 14: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1423/4/19 14

J/ radial flow

J/ radial flow consistent with 0, inconsistent with regeneration

AuAu: β=0, T=0.2+/-0.4, q-1=0.06+/-0.18CuCu: β=0, T=0.0+/-0.4, q-1=1.113+/-0.006pp: β=0, T=0.17+/-0.17, q-1=1.07+/-0.05

Page 15: Tsallis Fit to RHIC Data

Tsallis fit to high-pT

1523/4/19 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011

core

corona (pp)

Page 16: Tsallis Fit to RHIC Data

RAA & v2

23/4/19 STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 16

1) New extension to v2 still provide high quality fits – indicating bulk as a thermodynamic state. 2) Non-equilibrated component in the core produces a power-law tail in spectra and high v2 at the intermediate pT. 3) The baryon and meson yields are grouped in p+p.4) 2)+3) together bring down the bulk v2, produce the baryon enhancement and the NCQ scaling at the intermediate pT. 5) The medium quenches the jet (to fpp = 0.40), resulting in a finite v2 emission (9.4%).6) Data points at low pT dominates the fit 2.

Page 17: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1723/4/19 17

Summary

• Identified particle spectra at RHIC have been analyzed with Tsallis statistics in Blast-wave description to high pT

(light hadrons, multi-strange hadrons, charmonium)• Partonic phase

– Partons achieve thermal equilibrium in central heavy-ion collisions– J/ is not thermalized and disfavors regeneration

• Hadronic phase– Multi-strange hadrons decouple earlier – Hadronic rescattering doesn’t produce collective radial flow, but

drives the system off equilibrium– Radial flow reflects that when the multi-strange decouples

• Unified macroscopic description of hadron spectra/flow to high pT– Core and corona component

– Statistical originated NCQ scaling on RAA & v2

Page 18: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 1823/4/19 18

Thank you!

Page 19: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 19

Check— Parameter Correlation

23/4/19 19

<> = 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

Page 20: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 20

Check—Strangeness and light hadrons

23/4/19 20

Page 21: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 211/14/2010 21

Temperature fluctuation

1/1

/1/12

22

qT

TT

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

Reverse legend

23/4/19

Page 22: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 2223/4/19 22

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

Page 23: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 2323/4/19 23

How about radial flow?

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

Sizeable radial flow for heavy flavor decay electrons

Page 24: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 24

Beam energy dependence

23/4/19 24

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

Page 25: Tsallis Fit to RHIC Data

STAR-MTD Workshop, USTC, Mar 30 - Apr 1, 2011 2523/4/19 25

J/ radial flow

<> = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 2/nDof = 85.03 / 26