Non-Perturbative Effects in $\mu \to e \gamma$

TL;DR

This paper calculates non-perturbative effects of semileptonic tensor operators on the rare decay mu to e gamma and lepton dipole moments, setting new bounds on lepton-flavor violation using chiral perturbation theory.

Contribution

It introduces a novel application of chiral perturbation theory to compute non-perturbative contributions to lepton-flavor-violating processes without external hadronic particles.

Findings

Sets a bound of $ ext{Λ}_ ext{BSM} ext{ } extgreater 450$ TeV on semileptonic tensor operators.

Provides a method to relate non-perturbative QCD effects to leptonic observables.

Discusses potential applications to dark matter interactions.

Abstract

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q \sigma^{\mu \nu} q)(\bar \ell \sigma_{\mu \nu} \ell)$ to the purely leptonic process $\mu \to e \gamma$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $\mu \to e $ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $\Lambda_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions.