A consistent approach to bubble-nucleation theory

We summarize recent work on the consistent calculation of bubble-nucleation rates. Our approach is based on the notion of a real coarse-grained potential. The bubble-nucleation rate is calculated through an expansion around the semiclassical saddle point associated with tunnelling. We resolve outstanding problems related to the convexity of the potential, the double-counting of the effect of fluctuations and the inherent ultraviolet divergences. We determine the region of validity of the expansion around the saddle point. We find that this expansion fails near the spinodal line, and for weak or radiatively induced first-order phase transitions. We apply our method to the bound on the Higgs-boson mass from vacuum metastability and the electroweak phase transition. D eveloping a consistent theory of bubble nucleation is an important problem for particle and statistical physics. Possible applications include the description of most cosmological phase transitions, the questions of tunnelling in quantum mechanics and field theory, the problem of vacuum stability and its phenomenological consequences, the (currently unsatisfactory) explanation of the experimentally measured bubblenucleation rates for statistical systems, etc. The estimates of bubble-nucleation rates for first-order phase transitions are usually carried out within Langer’s theory of homogeneous nucleation [1], applied to relativistic field theory in refs. [2]. The nucleation rate is exponentially suppressed by the action (free energy rescaled by the temperature) of the critical bubble, a saddle point of the free energy of the system. Significant contributions to the nucleation rate may arise from higher orders in a systematic expansion around this saddle point. The first correction has the form of a pre-exponential factor that involves fluctuation determinants around the critical bubble and the false vacuum. The evaluation of this factor is a difficult problem at the conceptual and technical level, as crucial issues associated with the convexity of the potential, the divergences of the flucReport on work done in collaboration with A. Strumia and C. Wetterich. tuation determinants and the double-counting of the effect of fluctuations must be resolved.