Mass-dependence of pseudocritical temperature in mean field approximation

TL;DR

This paper investigates how the pseudocritical temperature in chiral phase transitions depends on quark mass within a mean field framework, analyzing various interaction models and their effects on critical behavior.

Contribution

It provides a detailed analysis of mass dependence of the pseudocritical temperature using different gluon interaction models in mean field approximation, highlighting the influence of interaction details.

Findings

Critical exponent matches 3D O(4) universality class.

Critical region size is up to 2-4 MeV in mean field approximation.

Dependence of chiral susceptibility and pion mass range on interaction kernel details.

Abstract

We restrict our computation in the mean field approximation which could lead to a clear critical behavior. We analyze the scaling behavior with different shape of interaction kernel by considering different dressed-gluon models. The critical exponent we obtained is consistent with that in the $3D$ $\textrm{O}(4)$ universality class. The size of critical region is up to $m_{0}^{} \le 2\sim 4\;$MeV in this mean field approximation which sets naturally an upper bound of the critical region since the fluctuations beyond mean-field usually diminish the critical region. Besides, we analyze the possible percentage of the maximum chiral susceptibility and pion mass range at which the chiral phase transition temperature is independent of the current quark mass. The results show that the percentage and the pion mass range depend on the details of interaction kernel, which differs in gluon models.