Quark Spectral Function and Deconfinement at Nonzero Temperature

TL;DR

This paper uses the maximum entropy method and Dyson-Schwinger equations to analyze the quark spectral function at finite temperature, identifying the deconfinement transition as a positivity restoration signal.

Contribution

It provides a self-consistent calculation of the quark spectral function at nonzero temperature, linking deconfinement and chiral symmetry restoration within a unified framework.

Findings

Deconfinement temperature is slightly below chiral restoration temperature.

Deconfinement and chiral symmetry restoration approximately coincide.

Spectral function positivity signals deconfinement transition.

Abstract

The maximum entropy method is used to compute the quark spectral function at nonzero temperature. We solve the gap equation of quantum chromodynamics (QCD) self-consistently, employing a rainbow kernel which phenomenologically models results from Dyson-Schwinger equations (DSE) and lattice QCD. We use the criterion of positivity restoration of the spectral function as a signal for deconfinement. Our calculation indicates that the critical temperature of deconfinement $T_d$ is slightly smaller than the one of chiral symmetry restoration $T_c$: $T_d\sim 94% T_c$ in the chiral limit, and $T_d\sim 96% T_c$ with physical light quark masses. Since these deviations are within the systematic error of our approach, it is reasonable to conclude that chiral symmetry restoration and deconfinement coincide at zero chemical potential.