Quasi-quark spectrum in the chiral symmetric phase from the Schwinger-Dyson equation

TL;DR

This paper non-perturbatively analyzes the fermion spectrum in the chiral symmetric phase using Schwinger-Dyson equations, revealing two broad peaks corresponding to quasi-fermion and plasmino, with thermal mass saturation at strong coupling.

Contribution

It introduces an analytic continuation method for the Schwinger-Dyson equation in the Feynman gauge to study fermion spectra non-perturbatively.

Findings

Fermion spectrum exhibits two broad peaks: quasi-fermion and plasmino.

Thermal mass saturates at strong coupling, with M ~ T.

Possible three-peak structure as a non-perturbative effect.

Abstract

We non-perturbatively study the fermion spectrum in the chiral symmetric phase from the Schwinger-Dyson equation with the Feynman gauge, in which we perform an analytic continuation of the solution on the imaginary time axis to the real time axis with a method employing an integral equation. It is shown that the fermion spectrum has two peaks, which correspond to the normal quasi-fermion and the plasmino, although these peaks in the strong coupling region are very broad, owing to multiple scatterings with gauge bosons. We find that the thermal mass of the quasi-fermion saturates at some value of the gauge coupling, beyond which the thermal (pole) mass satisfies $M \sim T$, independently of the value of the gauge coupling. We also comment on the appearance of a three-peak structure in the fermion spectrum as a non-perturbative effect.