Chiral Perturbation Theory with Virtual Photons and Leptons

TL;DR

This paper develops an extended chiral perturbation theory incorporating virtual photons and leptons to accurately describe isospin-breaking effects in semileptonic weak decays, providing a comprehensive low-energy framework.

Contribution

It introduces a novel effective field theory including light leptons as dynamical particles and calculates the associated one-loop divergences and counterterms.

Findings

Derived the full set of counterterms for the extended theory.

Applied the framework to pion and kaon leptonic decays.

Provided tools for precise low-energy weak interaction calculations.

Abstract

We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.