Two-particle Distribution and Correlation in Hot QGP

Two-particle Distribution and Two-particle Distribution and Correlation in Hot QGP Correlation in Hot QGP

Hui Liu （刘绘）Phys. Dep., JiNan University

Jiarong Li （李家荣）IOPP, CCNU

Outline:• Brief review on distribution functions

• Dispersion relations of HTL and complete one loop

• Oscillatory potential in complete one loop

• Radial distribution function and static structure function of hot QGP

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Distribution Functions (review)Distribution Functions (review) Distribution functionDistribution function

Probability of occurrence of a particular arrangement of particles

Radial distribution function (RDF)Radial distribution function (RDF)

Probability of finding two particles at a distance r from each other

ji

δN

rgρ )rrr(1

)( ji0

What can RDF tell us?What can RDF tell us? Spacial configuration of many-body system

Length of order

)r,,r,r( N21)( Nn

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Solid: long-range order Gas: completely randomLiquid: short-range order

Static structure function Fourier transformation

Can be measured by experiment

Basic quantity in atomic liquid theory, related to various observables

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How to obtain the RDFHow to obtain the RDF

From theory

Potential of mean force

From experiment

In atomic liquid, the structure function can be

measured by scattering experiment

Liquid Cl2from Egelstaff 1985

Contains both effects of dynamical interactions and thermal statistics

Incident beams sample

Scattered beams

kk 0

0kkq

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General form of static potentialGeneral form of static potential

Diagrammatic description

Analytic expression

General form with pole contribution

PotentialPotential

Effective propagator

obtained by resumming all possible irreducible diagrams

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QED one-loop polarizationQED one-loop polarization

Oscillatory potentialOscillatory potential

Find out the poles numerically and then

plot the static potential

Obvious damping oscillation of the static

potential in the completely one-loop

calculation, qualitatively different with

Debye form

HTL approximation, Debye screening

Complete one loop, q-dependent

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Dispersion RelationsDispersion Relations Dispersion relationDispersion relation

Energy-moment relation defined by the ze

ros of full propagator, which depends on t

he polarization patterns (dynamics) and th

ermodynamical environment

Vacuum (T＝ 0) ， qr＝ qi＝ 0

free particle

HTL (high T limit), qr＝ 0

Debye screening

HTL

one loop

free particle

Complete one loopComplete one loop

Lower plasma frequency

Threshold frequency

Damping oscillatory screening

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RDF in hot QGPRDF in hot QGP Gluon polarizationGluon polarization

RDF at complete one loopRDF at complete one loop

Short range order. Very similar to the

typical shape of liquid. Footprint of

liquid QGP!?

Enhanced peaks at lower temperatures.

0.5GeVT 0.40.3

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Structure FunctionStructure Function Fourier transformation of auto correlation functionFourier transformation of auto correlation function

Auto correlation function

Fourier transformation

Structure functionStructure function Prominent peak in momentum space

Space-time correlationSpace-time correlation Spectral representation of structure function

Sensitive spectrum regions, quasi-particle?

),(),0(),()0()( qωStρtrρρrρ

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SummarySummary Distribution function is describing the spacial configuration of a many-

body system which can be obtained via both theory and experiment.

We compared the dispersion relations of HTL and complete one loop,

pointing out an important discrepancy in the dynamical screening

regime which is responsible for the different static screening picture .

The RDF of hot QGP appears an obvious damping oscillation which

implies the QGP might be in a liquid state.

Static structure functions, which is the Fourier transformation of auto-

correlation function, can be measured by experiment. We hope in this

way the picture in our calculation can be tested by the experiments.

Any comments or suggestions are warmly welcome!


Back up slidesBack up slides


HTL approximationHTL approximation

The pole is purely imaginary

Soft modes of external line in HTL.

(high temperature limit)

All modes involved in complete

one-loop calculation.

Pole can be only chosen from the soft

modes in HTL approximation but from

all modes in complete one-loop

calculation.


One loopOne loop Static polarization tensor of QCDStatic polarization tensor of QCD

α

rq

iq Pole evolution with coupling Pole evolution with coupling

constantconstant T:1~2Tc α: 0.2~0.5

Two-particle Distribution and Correlation in Hot QGP

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