Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study

TL;DR

This paper advances the perturbative study of the SU(2) Yang-Mills deconfinement transition by calculating two-loop corrections to the effective potential, improving the accuracy of critical temperature predictions and thermodynamic properties.

Contribution

It provides the first two-loop calculation of the background field effective potential in SU(2) Yang-Mills theory, refining previous one-loop results.

Findings

Two-loop corrections improve the critical temperature estimate.

Thermodynamic pressure near the transition is significantly affected by two-loop contributions.

The Polyakov loop remains a reliable order parameter at higher-order calculations.

Abstract

In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading-order contribution in perturbation theory for the SU(2) case. In particular, we compute the background field effective potential at two-loop order and the corresponding Polyakov loop, a gauge invariant order parameter of the transition, at one-loop order. We show that the two-loop correction brings the critical temperature closer to its actual value as compared to the previous one-loop result. We also compute the thermodynamic pressure as a function of the temperature and show that two-loop contributions play an important role in the vicinity of the phase transition.