Elliptic flow of thermal photons in Au+Au collisions at 200GeV

QNP2009 Beijing, Sep 21 - 26, 2009

F.M. Liu Central China Normal University, China

T. Hirano University of Tokyo, Japan

K. Werner University of Nantes, France

Y. Zhu Central China Normal University, China

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Outline

• Motivations• Calculation approach• Results• Conclusion

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Motivations• The properties of the hot dense matter created in heavy ion collision are of great

interest, especially the critical behaviors.

• As penetrating probes, thermal photons can provide the inner information of the

plasma, which is a useful compensation to the signals of hadrons emitted from

the surface of the plasma.

• Questions: What can we learn from direct photon signals? How is

thermal photon signal, i.e. the elliptic flow, related to the system

evolution? …

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Calculation approachA precise calculation of direct photon productionrequires careful treatments on

• All sources of direct photons: from primordial scatterings at early stage, thermal photons, jet photon conversion, fragmentation contribution, …

• The space-time evolution of the created hot dense matter distributions of thermal partons thermal photons, low pt hadrons

• The propagation of jets in plasma (energy loss) distribution of hard partons high pt photons and hadrons

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thermal photon production

upETExdpdyd

dN

t

**thermal

42

thermal

),,(

2004 al,et Rapp R.

1991 al,et Kapusta:),( *HG TE

(2001) Yaffe& MooreArnold, :),( *QGP TE

Thermal parton interactions are considered in emission rate:

...effect LPM

qqg

qq

qqg

gqq

• In the local rest frame, photons are emitted from the thermal bath isotropically.

• Thermal photons’ v2 is caused by the Lorentz boost and accumulated with the space-time integration.

• Both the strength and the asymmetry of the transverse flow are important.

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the evolution of the matter

fm/c6.00

),,,,...(,,,, zyxBsup

Initial condition: thermalized QCD matter at

Freeze-out:

Evolution: 3D ideal hydrodynamic equation

described with 3+1D ideal hydrodynamics

0 T

MeV100~or fm/GeV08.0 3 thth T

MeV170cTEoS: 1st order phase transition at

QGP phase: 3 flavor free Q & G gas

HG phase: hadronic gas PCE

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Initial conditions at 0Flow velocity: zero

Energy density: (two options)

Parameterized based on Glauber model—a plateau is assumed. Hirano et al. Phys. Rev. C77:044909, 2008

EPOS model: based on string overlapping. K.Werner@SQM09

Uniform distribution is assumed along longitudinal direction in 2+1D hydrodynamics

Parameters constrained with PHOBOS data

Tested with hadrons’ yields, spectra, v2 and particles correlation

%) ,(d

dn

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Time evolution of the plasma

Energy-weighted Space-averaged

Energy density gets weaker with time.

Transverse flow gets stronger with time.

The asymmetry increases with eccentricity.22

22

2

22

yx

yxH

yxr

vv

vvv

vvv

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FML, T.Hirano, K.Werner, Y. Zhu Phys. Rev. C 79, (2009) 014905;

J. Phys. G 36 (2009) 064072.

Results: Pt spectra of direct photons

Direct photon production from AuAu collisions at top RHIC energy is well explained in a large pt range at all centralities. The effect from jet quenching is discussed.

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pt dependence of thermal photon v2

Elliptic flow of thermal photons decreases at high pt due to the abundant emission at early time.

FML, T.Hirano, K.Werner, Y. Zhu, Phys. Rev. C80,034905 (2009).

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Centrality dependence of pt-int. v2

Maximum appears at 40-50% centrality. Why?

Note:

The maximum of measured hadronic v2

also appears at this centrality,

but viscosity is needed to explain it.

Both strength and asymmetry of transverse flow are important.

Thermal photons dominant the low pt contribution and become the main part in the pt-integrated v2 of direct photons.

When compared with measurements, one should be careful with minimum pt.

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Rapidity dependence

The rapidity distribution can not identify different initial conditions;

But the elliptic flow of thermal photons “remembers” the initial conditions.

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Thermal photons from eta_s source Parameterized initial condition

EPOS initial condition

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Conclusion• Ideal hydro model can reproduce the measured pt spectra of direct photons at diff

erent centrality with the four sources we considered.

• Thermal photons’ v2 decreases at higher pt due to more fraction from early emissi

on.

• We predict thermal photons’ v2 reaches maximum at 40-50% centrality, due to the

interplay between the strength and asymmetry of the transverse flow. Contrary to

hadronic v2, no need of viscosity here.

• Thermal photons dominant the low pt contribution and become the main part in the

pt-integrated v2 of direct photons.

• Similar to hadronic signal, the rapidity distribution of thermal photons’ v2 can revea

l the initial longitudinal energy/entropy distribution.

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Thank you!

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Initial condition ： Glauber model

Parameterized rapidity distribution in pp collisions

Energy density or entropy distribution in the space:

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EPOS initial condition

Strings are constructed randomly in NN collisions. String segments overlap in the space and

form the core and corona region.

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thermal photons v2 time evolution

Fraction emitted at earlier timeIncreases with pt.

Elliptic flow of thermal photonsincreases with time.

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Dependence of EoS?

Elliptic flow is more sensitive to EoS than pt spectrum!

Various input of EoS

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QGP phase and HG phase

V2 from hadronic phase is much bigger than from QGP phase.

V2 can carry different information than pt spectrum.

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Pt spectrum from pp collisionsPRL 98, 012002 (2007)

A good test for contributions from leading order +fragmentation without Elossin AA collisions.

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Isosping mixture and nuclear shadowing:

RAA suppression from initial effect

),()]()(

)([)( /// AxRxGA

zAxG

A

zxG EKS

aNapaAa

)ˆˆˆ()(ˆ

ˆ),(),( 2

/2

/AB2

)LO(

utscdabtd

dsMxGMxGdxdxT

pdyd

dNbBb

abaAaba

t

AB

The dominant contribution at high pt is the LO contribution from NN collisions:

The isospin mixtureand nuclear shadowing reduce Raa at high pt.

This is the initial effect, not related to QGP formation.

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Distribution of hard partons

)ˆˆˆ()(ˆ

ˆ),(),( 2

/2

/AB2

jet

utscdabtd

dsMxGMxGdxdxTK

pdyd

dNbBb

abcdaAaba

t

AB

),()()()( /// AxRxGA

ZxG

A

NxG EKS

apaNaAa

MRST 2001 LO pDIS and EKS98 nuclear modification are employed

)(),2

(),2

(),(30 zy

bxTy

bxT

pd

dNrpf BA

Jet phase space distribution at τ=0:

)(),(),,(),( 00003 Evpptvrpfpdrpfxpf

at τ>0:

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Why jets lose energy

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Fix D with pi0 suppression • From pp collisions:

• From AA collisions, parton energy loss is considered

via modified fragmentation function

),(1 20

/2t

2,t

2

0

QzDzpdyd

dNdz

pdyd

dNcc

c

cpp

gqcc

pp

Factorization scale and renormalization scale to be tpQM

functionion fragmentat KKP :),( 20/ QzD cc

),,( 2/ ccc EQzD X.N.Wang’s formula

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Parton Energy Loss in a Plasma

• Energy loss of parton i=q, g,

• Energy loss per unit distance, i,e, with BDMPS

D: free parameter

• Every factor depends on the location of jet in plasma , i.e.,

0

))(,())(,,( ),,( 00 rfridrpiE QGP

is EDri / ))(,,( *2

)/8ln()233(

6)(

cfs TTN

T

upE *

)(r

fQGP: fraction of QGP at a given point

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Fix D with pi0 suppression

A common D=1.5for various Centralities!