Chiral restoration at finite temperature with meson loop corrections

TL;DR

This paper studies how chiral symmetry in QCD is restored at finite temperature for two flavors, emphasizing the importance of meson-loop corrections in reproducing the correct phase transition behavior.

Contribution

It introduces meson-loop corrections into a finite-temperature instanton model to accurately describe chiral-restoration patterns beyond the chiral limit.

Findings

MLC are crucial for correct universality-class behavior.

Chiral transition is second-order at zero quark mass.

Transition temperature increases with quark mass.

Abstract

We investigate chiral-restoration patterns of QCD for N_{c}=3 and N_{f}=2 at finite temperature (T) and zero quark-chemical potential beyond the chiral limit, indicating the explicit chiral-symmetry breaking. To this end, we employ the instanton-vacuum configuration for the flavor SU(2) sector and the Harrington-Shepard caloron for modifying relevant instanton parameters as functions of T. The meson-loop corrections (MLC), which correspond to 1/N_{c} corrections, are also taken into account to reproduce appropriate m_{q} dependences of chiral order parameters. We compute chiral condensate as a function of T and/or m_{q}. From the numerical calculations, we observe that MLC play an important role to have a correct universality-class behavior of chiral-restoration patterns in this framework, depending on m_{q}: Second-order phase transition in the chiral limit, m_{q}=0 and crossover for m_{q}>0. Without MLC, all the restoration patterns are crossover, due to simple saddle-point approximations. It turns out that T^{\chi}_{c}=159 MeV in the chiral limit and T^{\chi}_{c}=(177,186,196) MeV for m_{q}=(5,10,15) MeV, using the phenomenological choices for the instanton parameters at T=0.