Decay Rate of Electroweak Vacuum in the Standard Model and Beyond

TL;DR

This paper presents a precise, gauge-invariant calculation of the electroweak vacuum decay rate in the Standard Model and beyond, accounting for uncertainties and extending to models with classical scale invariance.

Contribution

It introduces a new technique for calculating the decay rate of a false vacuum at one-loop level, including zero mode effects, and provides an analytic and fitting formula applicable to various models.

Findings

Estimated decay rate of the electroweak vacuum with uncertainties.

Analytic formula applicable to models with high-energy scale scale invariance.

Discussion of effects of extra fermions on vacuum stability.

Abstract

We perform a precise calculation of the decay rate of the electroweak vacuum in the standard model as well as in models beyond the standard model. We use a recently-developed technique to calculate the decay rate of a false vacuum, which provides a gauge invariant calculation of the decay rate at the one-loop level. We give a prescription to take into account the zero modes in association with translational, dilatational, and gauge symmetries. We calculate the decay rate per unit volume, $\gamma$, by using an analytic formula. The decay rate of the electroweak vacuum in the standard model is estimated to be $\log_{10}\gamma\times{\rm Gyr~Gpc^3} = -582^{+40~+184~+144~+2}_{-45~-329~-218~-1}$, where the 1st, 2nd, 3rd, and 4th errors are due to the uncertainties of the Higgs mass, the top quark mass, the strong coupling constant and the choice of the renormalization scale, respectively. The analytic formula of the decay rate, as well as its fitting formula given in this paper, is also applicable to models that exhibit a classical scale invariance at a high energy scale. As an example, we consider extra fermions that couple to the standard model Higgs boson, and discuss their effects on the decay rate of the electroweak vacuum.