Generalized Heisenberg-Euler formula in Abelian gauge theory with parity violation

TL;DR

This paper derives a generalized Heisenberg-Euler formula for Abelian gauge theories with parity violation, enabling analysis of vacuum birefringence experiments probing dark sectors with non-parity-conserving interactions.

Contribution

It extends the Heisenberg-Euler formula to include parity-violating axial vector couplings in Abelian gauge theories, providing a theoretical basis for new experimental probes.

Findings

Derived a formula applicable to parity-violating theories

Expressed spin-related factors via expectation values in background fields

Facilitates analysis of vacuum magnetic birefringence experiments

Abstract

A generalized Heisenberg-Euler formula is given for an Abelian gauge theory having vector as well as axial vector couplings to a massive fermion. So, the formula is applicable to a parity-violating theory. The gauge group is chosen to be $U(1)$. The formula is quite similar to that in quantum electrodynamics, but there is a complexity in which one factor (related to spin) is expressed in terms of the expectation value. The expectation value is evaluated by the contraction with the one-dimensional propagator in a given background field. The formula affords a basis to the vacuum magnetic birefringence experiment, which aims to probe the dark sector, where the interactions of the light fermions with the gauge fields are not necessarily parity conserving.