Quark Number Susceptibilities from Two-Loop Hard Thermal Loop Perturbation Theory

TL;DR

This paper computes quark number susceptibilities using two-loop hard thermal loop perturbation theory, providing semi-analytic results and comparisons with other QCD approaches to understand quark-gluon plasma properties.

Contribution

It introduces a semi-analytic method for calculating quark number susceptibilities at two-loop order in HTL perturbation theory, extending previous leading-order results.

Findings

Results agree with lattice QCD at small chemical potential.

Provides analytic expressions for susceptibilities at leading and next-to-leading order.

Shows consistency with other perturbative and non-perturbative QCD calculations.

Abstract

We use the recently obtained two-loop hard thermal loop perturbation theory thermodynamics functions of a plasma of quarks and gluons to compute the diagonal second- and fourth-order quark number susceptibilities. The two-loop hard thermal loop perturbation theory thermodynamic functions used are reliable in the limit that the ratio of the quark chemical potential to temperature is small. Using this result, we are able to obtain (semi-)analytic expressions for the quark number susceptibilities at leading- and next-to-leading-order in hard thermal loop perturbation theory. We compare the hard thermal loop perturbation theory results with perturbative quantum chromodynamics calculations, a Polyakov-loop Nambu-Jona-Lasinio model calculation, and lattice quantum chromodynamics results.