Hot QCD equations of state and response functions for quark-gluon plasma

TL;DR

This paper investigates the response functions and screening effects in quark-gluon plasma using two different equations of state, revealing significant deviations from ideal behavior and aligning well with lattice QCD results for quarkonium dissociation.

Contribution

It introduces a method to compute chromo-electric susceptibilities using effective chemical potentials within two QCD equations of state, incorporating non-perturbative effects and comparing with lattice data.

Findings

Chromo-electric susceptibilities deviate significantly from ideal plasma predictions.

Medium effects modify heavy quark potential and screening lengths.

Dissociation temperatures for quarkonium states agree with lattice QCD results.

Abstract

We study the response functions (chromo-electric susceptibilities) of quark-gluon plasma as a function of temperature in the presence of interactions. We consider two equations of state for hot QCD. The first one is fully perturbative, of $O(g^5)$ EOS and, and the second one which is $O[g^6\ln(1/g)+\delta]$, incorporates some non-perturbative effects. Following a recent work (Physical Review {\bf C 76}, 054909(2007)), the interaction effects contained in the EOS are encapsulated in terms of effective chemical potentials($\tilde\mu$) in the equilibrium distribution functions for the partons.By using them in another recent formulation of the response functions({\tt arXiv:0707.3697}), we determine explicitly the chromo-electric susceptibilities for QCD plasma. We find that it shows large deviations from the ideal behavior. We further study the modification in the heavy quark potential due to the medium effects. In particular, we determine the temperature dependence of the screening lengths by fixing the effective coupling constant $Q$ which appears in the transport equation by comparing the screening in the present formalism with exact lattice QCD results. Finally, we study the dissociation phenomena of heavy quarkonium states such as $c\bar{c}$ and $b\bar{b}$, and determine the dissociation temperatures. Our results are in good agreement with recent lattice results.