Two-particle Distribution and 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

USTC 0807 Hui Liu 2 Distribution Functions (review) Distribution function Distribution 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 What can RDF tell us? What can RDF tell us?  Spacial configuration of many-body system  Length of order

USTC 0807 Hui Liu 3 Solid: long-range order Gas: completely random Liquid: short-range order  Static structure function Fourier transformation Can be measured by experiment  Basic quantity in atomic liquid theory, related to various observables

USTC 0807 Hui Liu 4 How to obtain the RDF How 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 Cl 2 from Egelstaff 1985 Contains both effects of dynamical interactions and thermal statistics Incident beams sample Scattered beams

USTC 0807 Hui Liu 5 General form of static potential General form of static potential  Diagrammatic description  Analytic expression  General form with pole contribution Potential Effective propagator obtained by resumming all possible irreducible diagrams

USTC 0807 Hui Liu 6 QED one-loop polarization QED one-loop polarization Oscillatory potential Oscillatory 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

USTC 0807 Hui Liu 7 Dispersion Relations Dispersion relation Dispersion relation  Energy-moment relation defined by the zeros of full propagator, which depends on the polarization patterns (dynamics) and thermodynamical environment  Vacuum (T ＝ 0) ， q r ＝ q i ＝ 0 free particle  HTL (high T limit), q r ＝ 0 Debye screening HTL one loop free particle Complete one loop Complete one loop  Lower plasma frequency  Threshold frequency  Damping oscillatory screening

USTC 0807 Hui Liu 8 RDF in hot QGP Gluon polarization Gluon polarization RDF at complete one loop RDF at complete one loop  Short range order. Very similar to the typical shape of liquid. Footprint of liquid QGP!?  Enhanced peaks at lower temperatures.

USTC 0807 Hui Liu 9 Structure Function Fourier transformation of auto correlation function Fourier transformation of auto correlation function  Auto correlation function  Fourier transformation Structure function Structure function  Prominent peak in momentum space Space-time correlation Space-time correlation  Spectral representation of structure function  Sensitive spectrum regions, quasi-particle?

USTC 0807 Hui Liu 10 Summary  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!

USTC 0807 Hui Liu 11 Back up slides

USTC 0807 Hui Liu 12 HTL 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.

USTC 0807 Hui Liu 13 One loop Static polarization tensor of QCD Static polarization tensor of QCD Pole evolution with coupling constant Pole evolution with coupling constant  T:1~2Tc α: 0.2~0.5