Two-particle Distribution and Correlation in Hot QGP

1. 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

2. Distribution Functions (review) • Distribution function • Probability of occurrence of a particular arrangement of particles • Radial distribution function (RDF) • Probability of finding two particles at a distance r from each other • What can RDF tell us? • Spacial configuration of many-body system • Length of order Hui Liu

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

4. Contains both effects of dynamical interactions and thermal statistics • 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 Incident beams Scattered beams sample Liquid Cl2 from Egelstaff 1985 Hui Liu

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

6. QED one-loop polarization • HTL approximation, Debye screening • Complete one loop, q-dependent • 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 Hui Liu

7. HTL one loop free particle Dispersion Relations • 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)， qr＝ qi＝0 free particle • HTL (high T limit), qr＝0 Debye screening • Complete one loop • Lower plasma frequency • Threshold frequency • Damping oscillatory screening Hui Liu

8. RDF in hot QGP • Gluon polarization • 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. Hui Liu

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

11. Back up slides Hui Liu

12. HTL approximation • 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. The pole is purely imaginary Hui Liu

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