Bubble-nucleation rates for radiatively induced first-order phase transitions

We present a consistent calculation of bubble-nucleation rates in theories of two scalar fields. Our approach is based on the notion of a coarse-grained free energy that incorporates the effects of fluctuations with momenta above a given scale k. We establish the reliability of the method for a variety of two-scalar models and confirm the conclusions of previous studies in one-field theories: Langer's theory of homogeneous nucleation is applicable as long as the expansion around the semiclassical saddle point associated with tunnelling is convergent. This expansion breaks down when the exponential suppression of the rate by the saddle-point action becomes comparable to the pre-exponential factor associated with fluctuations around the saddle point. We reconfirm that Langer's theory is not applicable to the case of weakly first-oder phase transitions. We also find that the same is true in general for radiatively induced first-order phase transitions. We discuss the relevance of our results for the electroweak phase transition and the metastability bound on the Higgs-boson mass.