Resummation of Vacuum Bubble Diagrams in Gaussian Propagator Model

TL;DR

This paper investigates the effectiveness of Borel resummation of vacuum bubble diagrams in accurately computing the decay width of a metastable vacuum, using a Gaussian propagator model with explicit high-order calculations.

Contribution

It provides an explicit analysis of the convergence of Borel resummation in a Gaussian model up to ninth-order vacuum bubble diagrams, offering insights into nonperturbative effects.

Findings

Borel resummation can reproduce the decay width in the Gaussian model.

Explicit ninth-order vacuum bubble calculations are performed.

The convergence behavior of the resummation is analyzed.

Abstract

An imaginary part of the false-vacuum energy density in a metastable system, i.e., the decay width due to quantum tunneling, might be reproduced by Borel resummation of vacuum bubble diagrams. We examine the convergence of this prescription in the Gaussian propagator model, in which the analytical expression of vacuum bubbles to the ninth order of loop expansion is available.