Neutral gluon polarization tensor in color magnetic background at finite temperature

TL;DR

This paper derives the structure of the neutral gluon polarization tensor in a magnetic background at finite temperature, providing detailed form factors and calculating key physical masses relevant for gluodynamics.

Contribution

It extends the tensor analysis of gluon polarization to finite temperature and magnetic backgrounds, including the derivation of form factors and non-transversal components.

Findings

Tensor structure includes ten components with seven transversal and three non-transversal.

Form factors are expressed as double parametric integrals and temperature sums.

Calculated Debye and magnetic masses of neutral gluons at high temperature.

Abstract

In the framework of SU(2) gluodynamics, we derive the tensor structure of the neutral gluon polarization tensor in an Abelian homogeneous magnetic field at finite temperature and calculate it in one-loop approximation in the Lorentz background field gauge. The imaginary time formalism and the Schwinger operator method are used. The latter is extended to the finite temperature case. The polarization tensor turns out to be non transversal. It can be written as a sum of ten tensor structures with corresponding form factors. Seven tensor structures are transversal, three are not. We represent the form factors in terms of double parametric integrals and the temperature sum which can be computed numerically. As applications we calculate the Debye mass and the magnetic mass of neutral gluons in the background field at high temperature. A comparison with the results of other authors is done.