Exact one-loop false vacuum decay rate

TL;DR

This paper presents an exact calculation of the one-loop false vacuum decay rate for scalar fields in a specific potential, including detailed regularization and renormalization procedures.

Contribution

It provides a novel, exact one-loop decay rate calculation for a scalar field with a quartic-quartic potential, including regularization and explicit expansions.

Findings

Derived a finite, renormalized decay rate expression.

Provided simple expansions for thin and thick wall limits.

Regularized and computed the functional determinant explicitly.

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.