Thermodynamics and quark condensates of three-flavor QCD at low temperature

TL;DR

This paper uses three-flavor chiral perturbation theory to calculate QCD thermodynamics and quark condensates at low temperatures, extending to include electromagnetic effects and comparing with lattice data.

Contribution

It provides a detailed calculation of QCD thermodynamics at low temperatures up to order p^6, including electromagnetic effects, and combines chiral perturbation theory with the Hadron Resonance Gas model for improved accuracy.

Findings

Chiral perturbation theory converges well up to 150 MeV.

Combined $ m ext{ChPT}$ and HRG model agrees with lattice below 170 MeV.

Chiral crossover temperature estimated at 160.1 MeV.

Abstract

We use three-flavor chiral perturbation theory ($\chi$PT) to calculate the pressure, light and $s$-quark condensates of QCD in the confined phase at finite temperature to ${\cal O}(p^6)$ in the low-energy expansion. We also include electromagnetic effects to order $e^2$, where the electromagnetic coupling $e$ counts as order $p$. Our results for the pressure and the condensates suggest that $\chi$PT converges very well for temperatures up to approximately 150 MeV. We combine $\chi$PT and the Hadron Resonance Gas (HRG) model by adding heavier baryons and mesons. Our results are compared with lattice simulations an d the agreement is very good for temperatures below {170} MeV, in contrast to the results from $\chi$PT which agree with the lattice only up to $T\approx120$ MeV. Our value for the chiral crossover temperature is 160.1 MeV, which compares favorably to the lattice result of $157.3$ MeV.