Green’s function method for handling radiative effects on false vacuum decay

Abstract

We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the λΦ 4 theory, extended with N additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.

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

“…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].…”

Gauge-independence of tunneling rates

“…Our results (3.3) and (3.4) show that the fluctuation determinant can be resummed, with the effect of replacing the classical action with the false-vacuum effective action. Moreover, our formalism shows that, rather than perturbing around a classical bounce solution, one has to consider the full quantum bounce, as in the approach of [11]. Finally, expressing the tunneling rate in terms of the false-vacuum effective action and its solutions clarifies how to proceed when vacua or instabilities arise radiatively.…”

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

“…More specifically, in the thin-wall case, it arises because the bounce action is a maximum with respect to the radius of the critical bubble R. In fact, the negative eigenvalue is given by [14] …”

“…This approach has already been applied to examples in the thin-wall limit in Refs. [11,14,15]. Formally, these Green's functions are the inverse of the quadratic fluctuation operator, where the aforementioned zero modes must be projected out in order to leave the inversion well defined.…”