Erratum: False vacuum decay by self-consistent bounces in four dimensions [Phys. Rev. D75, 045001 (2007)]

Abstract

We compute bounce solutions describing false vacuum decay in a Φ 4 model in four dimensions with quantum back-reaction. The back-reaction of the quantum fluctuations on the bounce profiles is computed in the one-loop and Hartree approximations. This is to be compared with the usual semiclassical approach where one computes the profile from the classical action and determines the one-loop correction from this profile. The computation of the fluctuation determinant is performed using a theorem on functional determinants, in addition we here need the Green' s function of the fluctuation 1 e-mail: baacke@physik.uni-dortmund.de 2 e-mail: nina.kevlishvili@het.physik.uni-dortmund.de operator in oder to compute the quantum back-reaction. As we are able to separate from the determinant and from the Green' s function the leading perturbative orders, we can regularize and renormalize analytically, in analogy of standard perturbation theory. The iteration towards self-consistent solutions is found to converge for some range of the parameters. Within this range the corrections to the semiclassical action are at most a few percent, the corrections to the transition rate can amount to several orders of magnitude. The strongest deviations happen for large couplings, as to be expected. Beyond some limit, there are no self-consistent bounce solutions.2

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

“…This observation is true also of the Hartree approximation for the pure λΦ 4 theory analyzed numerically in Refs. [102][103][104][105]. Nevertheless, these additional two-loop diagrams remain subdominant compared to the O(λ 2 N ) and O(λ 2 N 2 ) contributions from the χ tadpole in Eq.…”

“…Thus, we anticipate that this methodical development may have numerical applications in the study of the decay rates of radiatively-generated metastable vacua, such as occur in the massless CW model [53] or the Higgs potential of the SM. Similar methods based upon Green's function techniques have been used previously to determine self-consistent bounce solutions numerically in the Hartree approximation of the pure λΦ 4 theory in both two and four dimensions [102][103][104][105].…”

Self-consistent solitons for vacuum decay in radiatively generated potentials

“…[27] to the * garbrecht@tum.de † p.millington@nottingham.ac.uk calculation of the one-loop tunneling rate in a model with spontaneous symmetry breaking (SSB) that arises purely radiatively via the Coleman-Weinberg mechanism [28]. Green's function methods have previously been applied to determine self-consistent bounce solutions in the Hartree-Fock approximation of the pure λΦ 4 theory [29][30][31][32]. This article represents a first exercise in the use of the Green's function method in Ref.…”

One-loop corrections to the string tension of the vortex in the Abelian Higgs model

“…In intermediate situations one may have recourse to a Hartree type approximation by including the back-reaction of the quantum fluctuations to the classical solution. The methods we use here are suitable for such investigations [26,27], or even for self-consistent calculations without classical solution [28] The text is organized as follows: In section 2 we present the model, the classical vortex solution and the classical string tension. In section 3 we relate in general the fluctuation operator to the one-loop correction to the string tension, and we explicitly derive the fluctuation operator.…”