ON THE PHASE-TRANSITION IN THE SCALAR THEORY

The basic tool for the study of the electroweak phase transition is V(eff)(phi, T), the one-loop finite-temperature effective potential, improved by all-loop resummations of the most important infrared contributions. In this paper we perform, as a first step towards a full analysis of the standard model case, a detailed study of the effective potential of the scalar theory. We show that subleading corrections to the self-energies lead to spurious terms, linear in the field-dependent mass m(phi), in the daisy-improved effective potential. Consistency at subleading order requires the introduction of superdaisy diagrams, which prevent the appearance of linear terms. The resulting V(eff)(phi, T) for the scalar theory hints at a phase transition which is either second-order or very weakly first-order.