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Jet Quenching in 1+1 Dimension Expanding Medium with Chemical Nonequilibrium

Inst. of Particle Phys., CCNUCheng LuanCheng LuanAugust,2004

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1. Introduction 2. Parton Evolution3. Jet Quenching in the 1+1 Expanding me

dium with Chemical Nonequilibrium

4. Numerical Results 5. Results

Outline

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I. IntroductionI. Introduction1.Motivation: Quark matter produced in Relativistic Heavy Ion Collision at RHIC: * system is expanding * system may be in chemical nonequalibrium

How about jet energy loss in the expansion system with chemical nonequalibrium?

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2. What is Jet Quenching?

hadrons

q

q

hadrons

leadingparticle suppressed

leading particle suppressed

E

Jet Quenching

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3. Why chemical non-equilibrium?

1) Gluons “thermalize” very rapidly, reaching approximately isotropic momentum space distributions after a time of the order of 0.2fm/c.

2) Full equilibration of the gluon phase –space density takes considerably longer.

Thermally equilibriumThermally equilibrium

Chemical non-Chemical non-equilibriumequilibrium

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II. Parton Evolution1.Assume that the QGP has thermally equilibrated but is off from chemical equilibrium(Jutter distribution)

If neglect the quantum corrections(Boltzmann approximation)

If the result is obtained for the factorized Bose distribution(MFD approximation)

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Thermal quark Debye mass:

MFD

Juttner

Boltzmann

Here we use MFD approximationHere we use MFD approximation

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Consider the dominant processes

The evolution of the parton densities governed by the master equations：

Assume the expansion of the parton fireball is purely longitudinal

For the1+1 dimension syestym ：

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2. If the matter is in thermal and chemical equilibrium.

the quark(antiquark) and gluon distribution function should be:

11)( /

Tpg epN

11)( /)(

Tpqq epN

For the 1+1 dimension system which is in thermodynamicalequilibrium,

0)(

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其中， 95.11 a 5.2fNfNb )3(2

921

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III.III. Jet Quenching in the 1+1 Expanding Medium with Jet Quenching in the 1+1 Expanding Medium with Chemical NonequilibriumChemical Nonequilibrium

k

x0 p

k

x0 p

Stimulated Emission Thermal Absorption

B-E Enhancement Factor

1+f(k)

Thermal Distribution Factor.

f(k)

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Final-state RadiationFinal-state Radiation

k

x0 p

k

x0 p

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Single direct rescattering:Single direct rescattering:

k

y0 y1 p

k

y0 y1 p

y0 y1 p

k

Double Born virtual interaction:

k

y0 y1 y1 p

y0 y1 y1 p

k

k

y0 y1 y1 p

y0 y1 y1 p

k

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reflects the destructive interference arising fromThe non-Abelian LPM effect.

Thus, the radiation probability at the fist order in opacity includingstimulated emission and thermal absorption is:

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In a 1+1 dimension expanding system, for a jet produced at

point , at time ,

The opacity in direction is:

Thus:

jet1

jet2

)( y

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The parton energy loss induced by rescattering at the first order

in opacity in the 1+1 dimension expanding medium become:

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fm2.00 fmL 5GevT 5.00 5.0

0g

Jet Energy loss in expansion system with chemical nonequalibrium

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• Intermediate large E, absorption is important

•Energy dependence becomes strong

•Very high energy E, net energy gain can be neglected

fm2.00 fmL 5GevT 5.00 5.0

0g

Detailed balance in expansion system with chemical nonequalibrium

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Jet Energy loss vs. initial fugacity

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If a parton produced at point , at time ,

loses the same energy in the equilibrated system as in the

non-equilibrated system when propagating in a static medium.

eqnoneq EE

What will happen if they propagate in a 1+1 expanding medium?

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•Parton energy loss in equilibrated system is larger than that in non-equilibrated system in the expansion medium.

•The ratio decreases with Increasing jet energy at fixed

•The ratio increases with Increasing at fixed E.

eqnoneq EE (in static medium)

0g

0gRatio of energy loss in expansion medium

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IV.Results1. Absorption is important at intermediate large E in

the 1+1 dimension expanding medium. Energy dependence becomes strong.

2. Parton energy loss is larger when the parton propagates in a equilibrated system than that in a chemical non-equilibrated system.

3. Parton energy loss in a chemical non-equilibrated system increases with E at fixed

4. The ratio of energy loss between equilibrated and non-equilibrated system decreases with increasing jet energy at fixed .The ratio increases with increasing at fixed E.

0g

0g

0g

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Thank YouThank You