# On the Decoupling Theorem for Vacuum Metastability

## TL;DR

This study investigates how heavy fields influence vacuum metastability and the applicability of the decoupling theorem in semiclassical tunneling processes, revealing scale-dependent effects on tunneling amplitudes.

## Contribution

It demonstrates that the decoupling theorem applies to partial tunneling amplitudes with fixed final configurations, depending on the bubble radius scale relative to heavy field masses.

## Key findings

- Decoupling applies to partial amplitudes, not total lifetime.
- Tunneling amplitudes for small bubbles are insensitive to heavy fields.
- Large bubbles' tunneling amplitudes can be significantly affected by heavy fields.

## Abstract

In this paper, we numerically study the impact heavy field degrees of freedom have on vacuum metastability in a toy model, with the aim of better understanding how the decoupling theorem extends to semiclassical processes. We observe that decoupling applies to partial amplitudes associated with fixed final state field configurations emerging from the tunneling processes, characterized by a scale such as the inverse radius of a spherically symmetric bubble, and not directly on the total lifetime (as determined by the "bounce"). More specifically, tunneling amplitudes for bubbles with inverse radii smaller than the scale of the heavier fields are largely insensitive to their presence, while those for bubbles with inverse radii larger than that scale may be significantly modified.