Fermion Spectrum at Ultrasoft Region in a Hot QED/QCD Plasma

TL;DR

This paper investigates the electron and quark spectral properties at ultrasoft momenta in high-temperature QED/QCD, confirming the existence of a specific pole in the propagator and analyzing gauge symmetry preservation.

Contribution

It establishes the presence of a pole in the ultrasoft region of the propagator and derives its properties, advancing understanding of spectral functions at extremely high temperatures.

Findings

Confirmed the pole at ultrasoft momentum in electron/quark propagator.

Derived the pole position as p_0=∓|p|/3-iζ with damping rate ζ.

Analyzed gauge symmetry preservation in the resummation scheme.

Abstract

An spectrum of an electron (quark) with ultrasoft momentum (p g^2T) is discussed at extremely high temperature in quantum electrodynamics (chromodynamics) with a resummed perturbation theory. We establish the existence of the pole suggested in the previous work of the electron (quark) propagator at ultrasoft region, and find that its pole position is p_0=\mp |p|/3-i\zeta, where \zeta is the damping rate which is of order g^2T ln 1/g, and the expression of its residue. We also discuss whether the resummation scheme preserves the gauge symmetry.