The elastic scattering of an atomic nucleus plays a central role in dark matter direct detection experiments. In those experiments, it is usually assumed that the atomic electrons around the nucleus of the target material immediately follow the motion of the recoil nucleus. In reality, however, it takes some time for the electrons to catch up, which results in ionization and excitation of the atoms. In previous studies, those effects are taken into account by using the so-called Migdal's approach, in which the final state ionization/excitation are treated separately from the nuclear recoil. In this paper, we reformulate the Migdal's approach so that the "atomic recoil" cross section is obtained coherently, where we make transparent the energy-momentum conservation and the probability conservation. We show that the final state ionization/excitation can enhance the detectability of rather light dark matter in the GeV mass range via the nuclear scattering. We also discuss the coherent neutrino-nucleus scattering, where the same effects are expected. *

The decay rate of the electroweak (EW) vacuum is calculated in the framework of the standard model (SM) of particle physics, using the recent progresses in the understanding of the decay rate of metastable vacuum in gauge theories. We give a manifestly gauge-invariant expression of the decay rate. We also perform a detailed numerical calculation of the decay rate. With the best-fit values of the SM parameters, we find that the decay rate of the EW vacuum per unit volume is about 10 −554 Gyr −1 Gpc −3 ; with the uncertainty in the top mass, the decay rate is estimated as 10Introduction: It is highly non-trivial whether the vacuum we are living in, which we call electroweak (EW) vacuum, is absolutely stable or not. If there exists a vacuum which has lower energy density than that of the EW vacuum, which is the case in a large class of particle-physics models, the EW vacuum decays via the quantum tunneling effect. If the decay rate is too large, the universe should have been experienced a phase transition before the present epoch, with which the universe would show completely different aspects than the present one. From the particle-physics and cosmology points of view, the stability of the EW vacuum is of particular interest to have deep insight into particle-physics models and the nature of the universe. Even in the standard model (SM) of particle physics, which is extremely successful to explain particle interactions, the EW vacuum may be metastable [1][2][3][4][5][6][7]. In particular, the discovery of the Higgs boson by the LHC experiments [8,9] shed light on the stability of the EW vacuum. The observed value of the Higgs mass suggests that the Higgs quartic coupling becomes negative via the renormalization group (RG) effects at energy scale much higher than the EW scale. This fact implies that the Higgs potential becomes negative and that the EW vacuum is not absolutely stable if the SM is valid up to a scale much higher than the EW scale.The decay rate of the EW vacuum has been estimated in the past, mostly using the method given in [10][11][12]. The decay rate of the metastable vacuum (i.e., false vacuum) per unit volume, which we call γ, is given in the following form:

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 oneloop 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, γ, by using an analytic formula. The decay rate of the electroweak vacuum in the standard model is estimated to be log 10 γ × Gyr Gpc 3 ¼ −582 þ40þ184þ144þ2 −45−329−218−1 , where the first, second, third, and fourth 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.

Abstract:The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter ξ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.

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