Probing μ e γ γ contact interactions with μ → e conversion

Contact interactions of a muon, an electron and two photons can contribute to the decay μ→eγγ, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the μ→e conversion rate, and show that for the coefficients of operators involving the combination FF∝|E→|2 (as opposed to FF˜∝E→·B→), the current bound on μ→e conversion is more sensitive than the bound on μ→eγγ.