Groundstate projection of the charged SU(2) polarization tensor in a chromomagnetic background field

TL;DR

This paper calculates the polarization tensor of a charged gluon in SU(2) within a chromomagnetic background, providing numerical methods and analyzing high-temperature effects to show stabilization of the ground state.

Contribution

It introduces a simplified representation of the polarization tensor and evaluates the charged gluon magnetic mass at high temperature, advancing understanding of gluon behavior in magnetic fields.

Findings

Polarization tensor expressed as a double parametric integral

Numerical evaluation methods for the polarization tensor

Charged gluon magnetic mass calculated at high temperature

Abstract

We consider the polarization tensor of a color charged gluon field in SU(2) in the background of a homogeneous color magnetic field and calculate its projection onto the lower (tachyonic) state. We obtain a quite simple representation of the polarization tensor in terms of double parametric integral. We provide examples for the numerical evaluation of the polarization tensor in this case. Also, we consider the corresponding expressions at high temperature and calculate the charged gluon magnetic mass in this limit. We conclude that radiation corrections stabilize the ground state. Applications of the results obtained are discussed.