State-of-the-Art Calculation of the Decay Rate of Electroweak Vacuum in the Standard Model

Abstract

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:

Impact of new physics on the EW vacuum stability in a curved spacetime background

“…The prescription for such a computation was finally given in [48]. Successively, in [49,50] the results of the latter analysis were applied to the computation of the EW vacuum decay rate in the SM.…”

“…Clearly the goal is no longer to derive bounds on its mass, but rather to perform more refined analyses that should allow to discriminate between absolute stability or metastability for the EW vacuum [18][19][20][21], to study the cosmological impact of the vacuum stability condition during and after inflation [22][23][24][25][26][27][28][29][30][31][32], and to test the impact that different NP scenarios can have on the vacuum stability condition [18,[33][34][35][36][37][38][39][40][41][42][43][44]. This renewed interest also prompted a more careful treatment of issues as the gauge invariance of the vacuum decay rate and the contribution of zero modes to the quantum fluctuation determinant [45][46][47][48][49][50].…”

Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

“…This allows us to find solutions that cannot be constructed perturbatively from classical solutions in the present case because the parameter R for the Fubini-Lipatov instanton is unknown a priori. In contrast, previous methods determine the radius R by selecting the scale where the running scalar coupling reaches its minimum, which then also minimizes the tunneling action [3,5,6]. Note that such an approach is not applicable to the example discussed in this paper, where only scalar loops are included, such that the scalar coupling is monotonically increasing.…”

“…While the problem of tunneling in classically scaleinvariant scalar theory has been addressed in a number of earlier articles [3][4][5][6]19], the present method is complementary in the following aspects:…”

“…A sufficiently large lifetime of metastable vacuum states [1,2] is an important criterion for the viability of models of electroweak symmetry breaking [3][4][5][6]. For other sectors that are more or less closely tied to the electroweak one, false vacuum decay can play an essential role in cosmology [7].…”