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.
Highlights
In the standard model (SM) of particle physics, it has been known that the Higgs quartic coupling may become negative at a high scale through quantum corrections, so that the Higgs potential develops a deeper vacuum
II, we summarize the formulation for the decay rate at the oneloop level, where we provide an analytic formula for each field that couples to the Higgs boson
We study the decay rate of a false vacuum whose instability is due to an renormalization group (RG) running of the quartic coupling constant of a scalar field, Φ
Summary
In the standard model (SM) of particle physics, it has been known that the Higgs quartic coupling may become negative at a high scale through quantum corrections, so that the Higgs potential develops a deeper vacuum. The dominant suppression of the decay rate comes from B, the prefactor A is important This is because of large quantum corrections from the top quarks and the gauge bosons. A prescription for the treatments of the gauge zero modes was developed [28,29], based on which a complete calculation of the decay rate of the EW vacuum became possible. There, we see that one-loop corrections from the top quark and the gauge bosons are very large there is an accidental cancellation It shows the importance of A for the evaluation of a decay rate.
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