Radiative Corrections in Yang-Mills thermodynamics

We provide arguments why the loop expansion of the pressure in the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics is likely to terminate at a finite order despite the fact that the effective gauge coupling is large (e≥√(8)π). Each order l of the expansion measures the lth power of the fraction of a typical residual action of the quantum fluctuation in one loop Sl and h. Here Sl rapidly decreases with l. This is demonstrated by a computation of irreducible 2-loop and 3-loop diagrams which correct the pressure of free quasiparticles radiatively. In fact, at the three-loop level, one diagram vanishes identically. By benchmarking with known 2-loop results we show that the Monte-Carlo method used to compute on the 3-loop level is reliable.