  Perturbation theory at finite temperature suffers from well-known infrared
problems. In the standard model, as a result, one cannot calculate the
effective potential for arbitrarily small values of $\phi$, the Higgs
expectation value. Because the Higgs field is now known not to be extremely
light, it is necessary to determine whether perturbation theory is a reliable
guide to properties of the weak phase transition. In this note, we evaluate the
most singular contributions to the potential at two loops as well as the
leading strong interaction contributions. Above the critical temperature, the
strong interaction corrections are reasonably small, while the weak corrections
are about 10\%, even for rather small values of the Higgs field. At the
critical temperature, the weak corrections have a more substantial effect,
rendering the transition significantly more first order, but not significantly
changing the upper bound on the Higgs mass required for baryogenesis.

High Energy Physics - Phenomenology