Resummation of Vacuum Bubble Diagrams in Gaussian Propagator Model

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.