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

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