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

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 $\mu \to e\gamma \gamma$.

14 pages, version accepted for publication