A fresh look at the calculation of tunneling actions in multi-field potentials

Abstract

The quantum decay of a metastable vacuum is exponentially suppressed by a tunneling action that can be calculated in the semi-classical approximation as the Euclidean action of a bounce that interpolates between the false and true phases. For multi-field potentials, finding the bounce is non-trivial due to its peculiar boundary conditions and the fact that the action at the bounce is not a minimum but merely a saddle point. Recently, an alternative tunneling action has been proposed that does not rely on Euclidean bounces and reproduces the standard result at its minimum. Here we generalize this new approach for several scalar fields and demonstrate how its use can significantly improve the numerical calculation of tunneling actions for multi-field potentials. arXiv:1811.09185v1 [hep-th]

A landscape for the cosmological constant and the Higgs mass

“…The bounce actions and trajectories are easily computed implementing the method of[22,23]. Our results agree with results obtained running the public code of[24], based on a different method.…”

The electroweak phase transition: a collider target

“…In principle, a fully non-perturbative computation of γ N (T ) would circumvent this difficulty, though it is computationally more involved. In the interim, semi-analytic approaches that may be useful in the context of perturbation theory are being explored [162,163]. Further research in this direction is clearly called for.…”

Simple gradient flow equation for the bounce solution

“…Also, public codes to calculate the bounce solution are available, such as CosmoTransitions [14,15], AnyBubble [16], and BubbleProfiler [17,18]. There are some works to discuss the bounce solution/action avoiding the direct calculation, e.g., some approximations [19][20][21], upperbounds [22][23][24], lowerbounds, [24][25][26], and an alternative formulation [27][28][29].…”