Bounce in Valley: Study of the extended structures from thick-wall to thin-wall vacuum bubbles

TL;DR

This paper investigates the valley structure in quantum meta-stability, introducing a new valley equation to analyze vacuum bubble structures, revealing the coexistence of thick-wall and thin-wall bubbles and their roles in decay processes.

Contribution

The study develops a new valley equation for quantum meta-stability analysis and numerically explores the structure of vacuum bubbles, highlighting the coexistence of different bubble configurations.

Findings

The valley contains both bounce solutions and other bubble structures.

Thick-wall bubbles have outer regions characterized by large-radius, thin-wall bubbles.

Smaller bubbles contribute to decay at higher energies.

Abstract

The valley structure associated with quantum meta-stability is examined. It is defined by the new valley equation, which enables consistent evaluation of the imaginary-time path-integral. We study the structure of this new valley equation and solve these equations numerically. The valley is shown to contain the bounce solution, as well as other bubble structures. We find that even when the bubble solution has thick wall, the outer region of the valley is made of large-radius, thin-wall bubble, which interior is occupied by the true-vacuum. Smaller size bubbles, which contribute to decay at higher energies, are also identified.