Gluon polarization tensor in color magnetic background

TL;DR

This paper calculates the one-loop gluon polarization tensor in SU(2) gluodynamics within a magnetic background, revealing non-transversal components and providing a framework for numerical evaluation and potential applications.

Contribution

It presents the first detailed calculation of the gluon polarization tensor in a magnetic background, including non-transversal parts and explicit form factor representations.

Findings

The polarization tensor has ten tensor structures with four in the neutral and six in the charged sector.

Seven tensor structures are transversal, three are non-transversal.

Form factors are expressed as double parametric integrals suitable for numerical computation.

Abstract

In SU(2) gluodynamics we calculate the gluon polarization tensor in an Abelian homogeneous magnetic field in one-loop order in the Lorentz background field gauge. It turned out to be non transversal and consisting of ten tensor structures and corresponding form factors - four in color neutral and six in color charged sector. Seven tensor structures are transversal, three are not. The non transversal parts are obtained by explicit calculation. We represent the form factors in terms of double parametric integrals which can be computed numerically. Some examples are provided and possible applications are discussed.