General structure of gauge boson propagator and its spectra in a hot magnetized medium

TL;DR

This paper systematically constructs the gauge boson propagator structure in a hot magnetized medium, analyzing the dispersion relations and mode degeneracies in different magnetic field regimes using the hard thermal loop approximation.

Contribution

It provides a general formalism for the gauge boson two-point functions in a magnetized thermal medium, including mode analysis in strong and weak magnetic fields.

Findings

In a thermal medium, gauge bosons exhibit a plasmon and degenerate transverse modes.

Magnetic fields lift the degeneracy of transverse modes, resulting in three quasiparticle modes.

The formalism applies to both QCD and QED, aiding in thermo-magnetic corrections.

Abstract

Based on transversality condition of gauge boson self-energy we have systematically constructed the general structure of the gauge boson two-point functions using four linearly independent basis tensors in presence of a nontrivial background, i.e., hot magnetized material medium. The hard thermal loop approximation has been used for the heat bath to compute various form factors associated with the gauge boson's two point functions both in strong and weak field approximation. We have also analyzed the dispersion of a gauge boson (e.g., gluon) using the effective propagator both in strong and weak magnetic field approximation. The formalism is also applicable to QED. The presence of only thermal background leads to a longitudinal (plasmon) mode and a two-fold degenerate transverse mode. In presence of a hot magnetized background medium the degeneracy of the two transverse modes is lifted and one gets three quasiparticle modes. In weak field approximation one gets two transverse modes and one plasmon mode. On the other hand, in strong field approximation also one gets the three modes in Lowest Landau Level. The general structure of two-point function may be useful for computing the thermo-magnetic correction of various quantities associated with a gauge boson.