Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

TL;DR

This paper extends three-loop hard-thermal-loop perturbation theory calculations to finite temperature and isospin chemical potential in QCD, providing thermodynamic quantities and susceptibilities that can be compared with lattice QCD results.

Contribution

It presents the first three-loop HTLpt calculation of QCD thermodynamics at finite isospin chemical potential, including various thermodynamic observables and susceptibilities.

Findings

Calculated pressure, energy density, and entropy density at finite $ng$.

Determined trace anomaly and speed of sound at finite isospin chemical potential.

Computed isospin susceptibilities up to sixth order at zero $ng$.

Abstract

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $\mu_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $\mu_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $\mu_I$. The second, fourth, and sixth-order isospin susceptibilities are calculated at zero $\mu_I$. Our results can be directly compared to lattice QCD without Taylor expansions around $\mu_q=0$ since QCD has no sign problem at finite isospin chemical potential.