A Slavnov-Taylor identity and equality of damping rates for static transverse and longitudinal gluons in hot QCD

TL;DR

This paper derives a Slavnov-Taylor identity for the gluon polarization tensor in hot QCD and shows that, at next-to-leading order, the damping rates for static transverse and longitudinal gluons are equal, clarifying previous conflicting reports.

Contribution

It introduces a Slavnov-Taylor identity in hot QCD and demonstrates the equality of damping rates for static gluons at next-to-leading order in thermal perturbation theory.

Findings

Derived Slavnov-Taylor identity for gluon polarization tensor.

Proved equality of damping rates for static transverse and longitudinal gluons.

Resolved discrepancies in previous calculations of gluon damping rates.

Abstract

A Slavnov-Taylor identity is derived for the gluon polarization tensor in hot QCD. We evaluate its implications for damping of gluonic modes in the plasma. Applying the identity to next to the leading order in hard-thermal-loop resummed perturbation theory, we derive the expected equality of damping rates for static transverse and longitudinal (soft) gluons. This is of interest also in view of deviating recent reports of $\gamma_t(p=0)\neq\gamma_l(p=0)$ based on a direct calculation of $\gamma_l(p=0)$.