Thermal corrections to the gluon magnetic Debye mass

TL;DR

This paper calculates the gluon polarization tensor in a strong magnetic field at zero and high temperature, revealing how thermal and magnetic effects influence the gluon magnetic Debye mass and the tensor's infrared properties.

Contribution

It provides a detailed analysis of the gluon polarization tensor in a thermo-magnetic environment, including new results on thermal corrections to the magnetic Debye mass in different scale hierarchies.

Findings

At zero temperature, the polarization tensor reduces to a parallel structure with an imaginary part for non-zero quark mass.

In the high temperature regime, the polarization tensor remains infrared finite as the quark mass approaches zero.

Thermal corrections to the magnetic Debye mass are analyzed for different scale hierarchies.

Abstract

We compute the gluon polarization tensor in a thermo-magnetic environment in the strong magnetic field limit at zero and high temperature. The magnetic field effects are introduced using Schwinger's proper time method. Thermal effects are computed in the HTL approximation. At zero temperature, we reproduce the well-known result whereby for a non-vanishing quark mass, the polarization tensor reduces to the parallel structure and its coefficient develops an imaginary part corresponding to the threshold for quark-antiquark pair production. This coefficient is infrared finite and simplifies considerably when the quark mass vanishes. Keeping always the field strength as the largest energy scale, in the high temperature regime we analyze two complementary hierarchies of scales: $q^2\ll m_f^2\ll T^2$ and $m_f^2\ll q^2\ll T^2$. In the latter, we show that the polarization tensor is infrared finite as $m_f$ goes to zero. In the former, we discuss the thermal corrections to the magnetic Debye mass.