Tunneling in Quantum Field Theory and the Fate of the Universe

Abstract

We improve on the conventional approach for determining vacuum stability in Quantum Field Theory, developing a consistent perturbative expansion that is gauge, and scale independent. Using the Coleman-Weinberg model, we explicitly show how conventional perturbation theory breaks down due to higher-order loops being of the same size, and explain how resumming an infinite set of diagrams fixes the problem. Our consistent expansion is applied to the Standard Model, leading to a revised stability bound of $m_h^{\mbox{\tiny{pole}}}>(129.4\pm 2.3)$ GeV, which labels the Standard Model vacuum as metastable. We discuss in pedagogical detail, decay rates in Quantum Mechanics and in Quantum Field Theory. In particular, the application to metastable vacuum states. Beginning with the definition of decay and the relevant physical scales, we derive a formula for the decay rate in terms of the path integral. The conventional decay rate formula is discussed, and is shown to be in agreement with the semi-classical approximation of our formula. For both the classification of vacuum stability, and the calculation of the vacuum decay rate we explore the effect of short-distance physics.