Probing $\mu e \gamma \gamma$ contact interactions with $\mu \to e$ conversion

TL;DR

This paper investigates how contact interactions involving a muon, an electron, and two photons can lead to muon-to-electron conversion in nuclei, showing current bounds are more sensitive for certain operator types.

Contribution

It calculates the muon-to-electron conversion rate due to these contact interactions and compares sensitivities of different experimental bounds.

Findings

Current bounds on muon-to-electron conversion are more sensitive for operators involving electric field squared.

The study highlights the importance of specific operator structures in constraining new physics.

Muon decay to electron and two photons can be mediated by contact interactions with measurable effects.

Abstract

Contact interactions of a muon, an electron and two photons can contribute to the decay $\mu \to e \gamma \gamma$, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the $\mu \to e$ conversion rate, and show that for the coefficients of operators involving the combination $FF \propto |\vec{E}|^2$ (as opposed to $F\tilde{F} \propto \vec{E} \cdot \vec{B}$), the current bound on $\mu \to e$ conversion is more sensitive than the bound on $\mu \to e \gamma \gamma$.