Gluon polarization tensor in a magnetized medium: Analytic approach starting from the sum over Landau levels

TL;DR

This paper develops an analytic method to compute the one-loop magnetic correction to the gluon polarization tensor using Landau-level representation, validating results in strong and weak magnetic field limits relevant for heavy-ion collisions.

Contribution

It introduces a novel analytic approach starting from Landau levels to evaluate the gluon polarization tensor in a magnetic field, including vacuum contributions and tensor structure analysis.

Findings

Reproduces established results in strong and weak magnetic field limits

Isolates vacuum contributions from the zero-field limit

Shows spurious tensor terms do not affect the polarization tensor

Abstract

We present an analytic method to compute the one-loop magnetic correction to the gluon polarization tensor starting from the Landau-level representation of the quark propagator in the presence of an external magnetic field. We show that the general expression contains the vacuum contribution that can be isolated from the zero-field limit for finite gluon momentum. The general tensor structure for the gluon polarization also contains two spurious terms that do not satisfy the transversality properties. However, we also show that the coefficients of this structures vanish and thus do not contribute to the polarization tensor, as expected. In order to check the validity of the expressions we study the strong and weak field limits and show that well established results are reproduced. The findings can be used to study the conditions for gluons to equilibrate with the magnetic field produced during the early stages of a relativistic heavy-ion collision.