Evolution of QCD Coupling Constant at Finite Temperature in the Background Field Method

TL;DR

This paper investigates how the QCD coupling constant evolves at finite temperature using the background field method and one-loop renormalization group equations, highlighting discrepancies due to gauge choices and formalism differences.

Contribution

It provides a detailed analysis of the finite temperature evolution of QCD coupling, comparing results with existing literature and clarifying sources of discrepancies.

Findings

Discrepancies linked to gauge choices and formalism differences.

Identification of the impact of Lorentz invariance breaking.

Comparison of imaginary and real time formalism results.

Abstract

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the break-down of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.