VACUUM DECAY IN THEORIES WITH SYMMETRY-BREAKING BY RADIATIVE-CORRECTIONS

The standard bounce formalism for calculating the decay rate of a meta stable vacuum cannot be applied to theories in which the symmetry brea king is due to radiative corrections, because in such theories the tre e-level action has no bounce solutions. In this paper I derive a modif ied formalism to deal with such cases. As in the usual case, the bubbl e nucleation rate may be written in the form Ae(-B). To leading approx imation, B is the bounce action obtained by replacing the tree-level p otential by the leading one-loop approximation to the effective potent ial, in agreement with the generally adopted ad hoc remedy. The next c orrection to B (which is proportional to an inverse power of a small c oupling) is given in terms of the next-to-leading term in the effectiv e potential and the leading correction to the two-derivative term in t he effective action. The corrections beyond these (which may be includ ed in the prefactor) do not have simple expressions in terms of the ef fective potential and the other functions in the effective action. In particular, the scalar-loop terms which give an imaginary part to the effective potential do not explicitly appear; the corresponding effect s are included in a functional determinant which gives a manifestly re al result for the nucleation rate.