Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, $D$ dimensional O(N) symmetric $\phi^4$ model ($D<4$) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.