False vacuum decay beyond the quadratic approximation: summation of non-local self-energies

TL;DR

This paper advances the understanding of false vacuum decay by developing a formalism that includes non-local self-energy effects beyond the quadratic approximation, crucial for accurate decay rate calculations in quantum field theory.

Contribution

It introduces a coupled system of equations for the bounce and propagator using the 2PI effective action, including a semi-analytic self-energy expression at two loops, improving upon the Hartree approximation.

Findings

Hartree approximation often inadequate for decay rate calculations

Derived semi-analytic self-energy expression for scalar fields with cubic and quartic interactions

Established a framework for quantum-corrected bounce and fluctuation determinant computations

Abstract

Using the 2PI effective action formalism, we study false vacuum decay beyond the quadratic approximation of the path integral. We derive a coupled system of equations for the bounce and the propagator, and we compute a semi-analytic expression for the self-energy of a real scalar field with cubic and quartic interactions from the 2PI effective action truncated at two loops and without further approximations. Deriving numerical results, we can show that the Hartree approximation, where non-local contributions to the self-energy are neglected, is generally not justified. The procedure we develop is a key step towards the explicit computation of the quantum corrected bounce, the determinant of fluctuations about it and the decay rate in the presence of classical zero-modes that are lifted by quantum effects, e.g. classically scale-invariant models relevant for assessing the Higgs stability.