Ultrasoft fermion mode and off-diagonal Boltzmann equation in quark-gluon plasma at high temperature

TL;DR

This paper derives a generalized Boltzmann equation for ultrasoft quark excitations in high-temperature QCD, revealing new insights into quark dispersion, damping, and multi-point functions near equilibrium.

Contribution

It introduces a generalized Boltzmann equation for ultrasoft quark modes in QCD, connecting kinetic theory with resummed perturbation methods at extremely high temperatures.

Findings

Derived the GBE from Kadanoff-Baym equations for ultrasoft quarks.

Obtained dispersion relation, damping rate, and excitation strength.

Established the GBE's role in determining ultrasoft multi-point functions.

Abstract

We derive the generalized Boltzmann equation (GBE) near equilibrium from the Kadanoff-Baym equation for quark excitation with ultrasoft momentum (~g^2T, g: coupling constant, T: temperature) in quantum chromodynamics (QCD) at extremely high T, and show that the equation is equivalent to the self-consistent equation derived in the resummed perturbation scheme used to analyze the quark propagator. We obtain the expressions of the dispersion relation, the damping rate, and the strength of a quark excitation with ultrasoft momentum by solving the GBE. We also show that the GBE enables us to obtain the equation determining the n-point function containing a pair of quarks and (n-2) gluon external lines whose momenta are ultrasoft.