PHOTONS AND EVOLUTION OF A CHEMICALLY EQUILIBRATING AND EXPANDING QGP

AT FINITE BARYON DENSITY

Shanghai Institute of Applied PhysicsJiali Long, Zejun He, Yugang Ma et al.

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OutlineIntroductionCalculated Results Evolution of the system Photon productionSummary

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I. INTRODUCTION

Relativistic heavy ion collisions provide the opportunity to study the formation and evolution of the QGP. Photon production as a signature of the formation of the QGP in collisions had been studied by many researchers.

J.Kapusta, P.Lichard et al have studied the photon production in a QGP at finite temperature.

Traxler, Vija, and Thoma have computed the photon production rate of a QGP at finite quark chemical potential for a given temperature (also a given energy density) using the Braaten-Pisarski method.

C.T.Traxler, M.H.Thoma and M.Strickland have studied the photon production in a chemically equilibrating and longitudinally expanding baryon-free QGP system. ……………………………..

finite baryon density 3+1 D expansion

chemical non-equilibrium

The system we studied

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The partons suffer many collisions in the QGP system may attain kinetic equilibrium, but away from the chemical equilibrium. K.Geiger, T.S.Biro et al have studied the effect of the chemical equilibration on the dilepton production in baryon-free QGP.

N.Hammon, K.Geiger indicated: the initial system has finite baryon density.

Up to now, in calculations of photons and dileptons the evolutions of the chemically equilibrating QGP system are almost described as a longitudinal scaling expansion. To improve the description of the evolution, some authors have discussed the transverse expansion, and superimposed the transverse expansion on longitudinal expansion to study the effect of the evolution of the system on the production. For comparison with experiments it is necessary to study the photon production in a QGP system with full evolution.

The set of coupled relaxation equations

The conservations of energy-momentum, entropy and baryon number

Considering the chemical equilibration processes:

ggggg qqgg ssgg ssqq

0)( T 0)(

su 0)( nu

Then, we can get a set of coupled relaxation equations which describe the evolution of the chemically equilibrating QGP system with finite baryon density in a 3+1 dimensional space-time.

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The evolution of the QGP system

0)()(1

)(1

)( zqgpzqgprqgprqgpt vsvsr

vsrr

s

0)()(1

)(1

)( zbzbrbrbt vnvnr

vnrr

n

Relaxation equations

0)]}()([

)](1

)(1

[)()({)]}(

)([)](1

)(1

[)()({

zbrrbzz

rbbrbrrbtbzr

rzzrrrrtqgp

vvv

vr

vrr

vvnvT

vTvvTr

vrTr

vTvTs

(1)

(2)

(3)

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conservation of entropy

conservation of baryon number

conservation of energy-momentum for r direction

0)]}(1

)(1

[

)]()(1

[)(1

)({)]}(1

)(1

[)]()(1

[)()({

rbbrr

bzbzbbtbr

rrzztqgp

vr

vrr

v

vvr

vr

vnvTr

vrTr

vvTvTr

vTvTs

0)]}()(1

[

)]()(1

[)()({)]}(

)(1

[)]()(1

[)()({

vvr

v

vvr

vvnvT

vrTr

vvTvTr

vTvTs

bzzb

zbrrbrbzbtbz

zzrrzrzztqgp

(4)

(5)

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conservation of energy-momentum for φ direction

conservation of energy-momentum for z direction

])(1[2])(1[2

)1()()(1

)(1

)(

22

22

3

ss

ss

g

gg

sg

qq

qq

g

gg

qg

g

ggzgzgrgrgt

nn

nn

n

nnR

nn

nn

n

nnR

n

nnRvnvn

rvrn

rn

])(1[2

])(1[)()(1

)(1

)(

22

22

ss

ss

q

qq

sq

qq

qq

g

gg

qgzqzqrqrqt

nn

nn

n

nnR

nn

nn

n

nnRvnvn

rvrn

rn

])(1[2

])(1[)()(1

)(1

)(

22

22

ss

ss

q

qq

sq

ss

ss

g

gg

sgzszsrsrst

nn

nn

n

nnR

nn

nn

n

nnRvnvn

rvrn

rn

(8)

(7)

(6)

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master equation describing the evolution of gluon

master equation describing the evolution of quark

master equation describing the evolution of s quark

from the following processes:

quark annihilation

Compton scatterings

and

bremsstrahlung

inelastic pair annihilation

gqq

qqg qqg

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P.Arnold, G.D.Moore and L.G.Yaffe, J. High Enery Phys. 12 (2001) 09.

J.Kapusta, P.Lichard and D.Seibert, Phys. Rev. D 44 (1991) 2774.

The photon production

We here focus on discussing Au + Au central collisions at RHIC energies. We use the initial conditions obtained from the self-screened parton cascade (SSPC) model. We consider zero impact parameter cylindrically symmetric collisions only, do not expect significant collective motion and thus take the initial velocity in the radial direction vr = 0. The initial distributions are given by . Here, N is the free parameter, Ci0 stands for the initial values such as the initial temperature T0, quark chemical potentialμq0 and so on.

]})/()/[(exp{)0,,( 000NN

i ZzRrCzrE

II. CALCULATED RESULTS

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0 1 2 3 4 5 6

0

100

200

300

400

500

600

700

T(M

ev)

r/R0

0.25fm 0.35fm 0.45fm 0.55fm 0.65fm 0.75fm 0.85fm 0.95fm

Evolution of the system (1)

The initial values:

fm25.00 34.00 g

068.00 q 34.00 s3

0 /4.61 fmGeV1/ 00 Tq

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Different color curves denotes the calculated distributions of temperature in the r direction at evolution times t=0.25,0.35, 0.45, 0.55, 0.65, 0.75, 0.85 and 0.95fm

Evolution of the system (2)

0 1 2 3 4 5 6

0

100

200

300

400

500

600

700

r/R0

0.25fm 0.35fm 0.45fm 0.55fm 0.65fm 0.75fm 0.85fm 0.95fm

q(M

ev)

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The calculated distributions of quark chemical potential

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 0.25fm 0.35fm 0.45fm 0.55fm 0.65fm 0.75fm 0.85fm 0.95fm

r/R0

g

Evolution of the system (3)

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

r/R0

0.25fm 0.35fm 0.45fm 0.55fm 0.65fm 0.75fm 0.85fm 0.95fm q

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The calculated distributions of fugacities for quarks and gluons

Photon production (1)

30 /4.61 fmGeV

3,2,1/ 00 Tq

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1.0 1.5 2.0 2.5 3.0

10-9

10-8

10-7

10-6

10-5

/T=1 /T=2 /T=3

gqq

The calculated photon spectra for

1 2 3

10-7

10-6

10-5

10-4

10-3

/T=1 /T=2 /T=3

qgq

Photon production (2)

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1.0 1.5 2.0 2.5 3.0

10-9

10-8

10-7

10-6

10-5

10-4

/T=1 /T=2 /T=3

qqg

1.0 1.5 2.0 2.5 3.0

10-9

10-8

10-7

10-6

10-5

10-4

/T=1 /T=2 /T=3

inelastic pair annihilation

Edn

/d3 p(

GeV

-2)

E(GeV)

Photon production (3)

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1.0 1.5 2.0 2.5 3.0

10-7

10-6

10-5

10-4

10-3

bremsstrahlung

/T=1 /T=2 /T=3

Edn

/d3 p(

GeV

-2)

E(GeV)

1.0 1.5 2.0 2.5 3.0

10-5

10-4

10-3

10-2

/T=1 /T=2 /T=3

Edn

/d3 p(

GeV

-2)

E(GeV)

Photon production (4)

The total photon production decreases with the initial quark chemical potential.

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from a longitudinally expanding system from a 3+1D expanding system

1.0 1.5 2.0 2.5 3.010-8

10-7

10-6

10-5

10-4

10-3

/T=1 /T=2 /T=3

Edn

/d3 p(

GeV

-2)

E(GeV)

quicker cooling of the system

Lifetimes of the quark phase

for the longitudinally expanding system

3.47, 3.88 and 3.19 fm

for 3,2,1/ 00 Tq

0.697, 1.539 and 1.022 fm

for the 3+1D expanding system

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The photon production decreases with increasing the quark chemical potential(also μ/ T );

comparing with the results of the longitudinal expansion system, we have found that in the present evolution model there exist the transverse flow which leads to the quick cooling of the system, hence the photon yield is much lower than the one of the longitudinal expanding system;

therefore, the signal to background ratio of photons from a plasma created in a heavy-ion collision may decrease significantly.

III. SUMMARY

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