RING-DIAGRAM SUMMATIONS IN THE FINITE-TEMPERATURE EFFECTIVE POTENTIAL

There has been much recent interest in the finite-temperature effectiv e potential of the standard model in the context of the electroweak ph ase transition. We review the calculation of the effective potential w ith particular emphasis on the validity of the expansions that are use d. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electr oweak phase transition. However, in the high-temperature regime, the i nfrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram s ummation, and show that the standard model has a first-order phase tra nsition in the weak coupling expansion.