Probing $μe γγ$ contact interactions with $μ\to e$ conversion

Contact interactions of a muon, an electron and two photons can contribute to the decay $μ\to e γγ$, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the $μ\to e$ 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 $μ\to e$ conversion is more sensitive than the bound on $μ\to e γγ$.

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