Treating divergence in quark matter by using energy projectors

TL;DR

This paper introduces a method using energy projectors to compute the gluon self-energy in quark-gluon plasma, effectively handling divergences and enabling non-perturbative calculations of gluon screening masses.

Contribution

It presents a novel approach with quark energy projectors to isolate divergences and compute gluon self-energy without approximation in a quark-gluon plasma.

Findings

Divergences only appear in mixed modes and are medium independent.

The method reproduces known HTL/HDL results in the small gluon momentum limit.

Non-perturbative calculation of gluon Debye mass and thermodynamic potential.

Abstract

We calculate gluon self-energy using quark energy projectors in a general quark-gluon plasma. By separating the quark field into a positive- and a negative-energy mode, the quark loop constructed with the same mode is always convergent, and the divergence appears only in the mixed loop with different modes and is medium independent. After removing the divergence in vacuum, we obtain the one-loop gluon self-energy at finite temperature, chemical potential and quarks mass without approximation. With the method of quark loop resummation, we calculate non-perturbatively the gluon Debye mass and thermodynamic potential. In the limit of small gluon momentum in comparison with temperature, chemical potential and quark mass, our calculation comes back to the known HTL/HDL results in literature.