Abstract
We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.
Highlights
Tunneling phenomena are among the most fascinating physical processes
A bubble of true vacuum forms, expands quickly, collides with other bubbles and fills up the entire universe. Theoretical studies of such transitions were initiated by Langer [1] and applied to field theory by [2] and notably by Coleman [3]
Current aLIGO [20] and aVIRGO [21] observatories are operating at frequencies that are mostly insensitive to TeV scale first order phase transitions, but upcoming detectors, such as LISA [22,23], DECIGO [24] and BBO [25,26], will have the ability to test such scenarios
Summary
Tunneling phenomena are among the most fascinating physical processes. They initiate cosmological first order phase transitions, where an unstable ground state—a false vacuum (FV)—transforms into an energetically favorable one. The prefactor cancels the renormalization scale-dependence of the Euclidean action and stabilizes the bubble nucleation rate, see [78] for a recent work on the uncertainties regarding gravitational wave production. We find a simple formula, where the energy scale of the FV factorizes and the rest of the prefactor depends only on the ratios of vevs and quartic couplings between the false and true vacuum This setup can be considered as a benchmark for understanding the impact of finite one loop corrections, needed for a consistent evaluation of the total rate at one loop. The quartic-quartic potential has no classical scale invariance, we only have to remove the four translational zero modes, which is done by a perturbative deformation of the homogeneous solution This relates the dimensional prefactor to the energy scale in the theory and is proportional to the bounce action. VII and technical details are left to the Appendices A and B
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