Particle decay in false vacuum

TL;DR

This paper investigates how particles induce decay of a false vacuum, providing exact decay rates for bosons in any dimension and fermions in 1+1 dimensions, and resolving infrared issues in certain cases.

Contribution

It offers new analytical expressions for decay rates induced by particles, including a closed form for fermions in 1+1 dimensions and insights into infrared cancellations.

Findings

Decay rate formulas for bosons in any dimension.

Closed expression for fermion decay rate in 1+1 dimensions.

Infrared problem resolution via mode cancellation.

Abstract

We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the `master field' the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for a fermion we find a closed expression for the decay rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an infrared problem of one-loop correction to the decay rate of a boson is resolved due to a cancellation between soft modes of the field. We also find the boson decay rate in the `sine-Gordon staircase' model in the limits of strong and weak coupling.