Structures of the Massive Vector Boson Propagators at Finite Temperature Illuminated by the Goldstone Equivalence Gauge

TL;DR

This paper investigates how finite temperature affects massive vector boson propagators, revealing that Goldstone bosons partly recover and can be treated similarly to zero-temperature cases, simplifying thermal process calculations.

Contribution

It introduces a novel analysis of thermal corrections to vector bosons using the Goldstone equivalence gauge, highlighting the emergence of quasi-poles and simplified Feynman rules at finite temperature.

Findings

Goldstone bosons partly recover at finite temperature.

Part of the Goldstone boson becomes a branch cut, approximated by quasi-poles.

Simplified Feynman rules for thermal vector boson processes.

Abstract

Inspired by the Goldstone equivalence gauge, we study the thermal corrections to an originally massive vector boson by checking the poles and branch cuts. We find that part of the Goldstone boson is spewed out from the longitudinal polarization, becoming a branch cut which can be approximated by the "quasi-poles" in the thermal environment. In this case, physical Goldstone boson somehow partly recovers. We also show the Feynmann rules for the "external legs" of these vector boson as well as the recovered Goldstone boson, expecting to simplify the vector boson participated process calculations by adopting the similar "tree-level" logic as in the zero temperature situation. Gauge boson mixing case are also discussed. Similar results are shown in other gauges, especially in the $R_\xi$ gauge.