Distinguishing models with $\mu \to e $ observables

Upcoming experiments will improve the reach for the lepton flavour violating (LFV) processes $\mu \to e \gamma$, $\mu \to e \bar{e} e$ and $\mu A \to e A$ by orders of magnitude. We investigate whether this upcoming data could rule out some popular TeV-scale LFV models (the type II seesaw, the inverse seesaw and a scalar leptoquark) using a bottom-up EFT approach involving twelve Wilson coefficients that can in principle all be determined by experimental measurements. In this 12-dimensional coefficient space, each model can only predict points in a specific subspace; for instance, flavour change involving singlet electrons is suppressed in the seesaw models, and the leptoquark induces negligible coefficients for 4-lepton scalar operators. Using the fact that none of these models can populate the whole region accessible to upcoming experiments, we show that $\mu \to e$ experiments have the ability to rule them out.