On the nature of the electroweak phase transition

We perform a systematic discussion of the finite-temperature effective potential of the Standard Model, $\veff$, with particular emphasis on the resummation of the most important infrared contributions. We improve over the existing computations of $\veff$ by consistently including subleading contributions to the $T$-dependent effective masses of scalar and vector bosons. We show that, even at subleading order, $\veff$ does not contain terms linear in $\phi$, and that subleading corrections further weaken the first-order nature of the electroweak phase transition. Moreover, for $m_t \simgt 110 \gev$ we find a ($m_t$-dependent) critical value of the Higgs mass, $m_h~c \sim O(70 \gev)$, above which the phase transition becomes {\it second} order. We also discuss the range of validity of our approximations and some prospects for further improvements.