Abstract
For a scalar theory whose classical scale invariance is broken by quantum effects, we compute self-consistent bounce solutions and Green's functions. Deriving analytic expressions, we find that the latter are similar to the Green's functions in the archetypal thin-wall model for tunneling between quasi-degenerate vacua. The eigenmodes and eigenspectra are, however, very different. Large infrared effects from the modes of low angular momentum $j=0$ and $j=1$, which include the approximate dilatational modes for $j=0$, are dealt with by a resummation of one-loop effects. For a parametric example, this resummation is carried out numerically.
Highlights
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]
Since tunneling events do not correspond to extrema of the Minkowskian action, the calculation of the decay rates relies on Euclidean solitons, which are saddle point configurations often referred to as bounces [1]
The fluctuation modes around the solitons differ from those in calculations of effective potentials because they include the gradient corrections from the varying background, whereas, for the effective potential, one assumes a field configuration that is constant throughout spacetime
Summary
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]. [10]), we encounter a significant limitation of this method Such a situation occurs for models of radiative symmetry breaking, where the true vacuum only appears through loop corrections [11] or, as in the case of interest for the present work, for approximately scale-invariant models, where the scale of the radius of the nucleating bubbles is not known before consistently accounting for quantum effects. For a scalar theory with a negative quartic self-coupling, the classical solution, known as the Fubini-Lipatov instanton [12,13], contains a scale parameter that determines the radius of the nucleating bubbles, which is not fixed at tree level In this case, one needs to find the bounce solutions by computing radiative corrections to the equations of motion self-consistently within the bounce field configuration, which is the main objective of the present paper. The imaginary part present in the effective potential—which assumes a constant, homogeneous field configuration—is removed when we account for the gradients of the field
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