On critical scaling at the QCD N_f=2 chiral phase transition

TL;DR

This paper analyzes the critical behavior of the quark propagator near the chiral phase transition in two-flavor QCD, emphasizing the importance of pion and sigma back-reactions and deriving analytical scaling laws consistent with universality.

Contribution

It introduces a self-consistent approach to study the critical scaling of the quark propagator, incorporating pion and sigma back-reactions beyond mean field.

Findings

Derived analytical scaling behavior of the quark propagator.

Confirmed the importance of the pion dispersion relation near criticality.

Numerically verified the analytical results assuming the critical dispersion relation.

Abstract

We investigate the critical scaling of the quark propagator of N_f=2 QCD close to the chiral phase transition at finite temperature. We argue that it is mandatory to take into account the back-reaction effects of pions and the sigma onto the quark to observe critical behavior beyond mean field. On condition of self-consistency of the quark Dyson-Schwinger equation we extract the scaling behavior for the quark propagator analytically. Crucial in this respect is the correct pion dispersion relation when the critical temperature is approached from below. Our results are consistent with the known relations for the quark condensate and the pion decay constant from universality. We verify the analytical findings also numerically assuming the critical dispersion relation for the Goldstone bosons.