Abstract
In Effective Field Theory, we describe $\mu \leftrightarrow e$ flavour changing transitions using an operator basis motivated by experimental observables. This implies that $\mu \rightarrow e_L \gamma $, $\mu \rightarrow e_L \bar{e} e$ and $\mu \rightarrow e_L$ conversion on nuclei probe a six-dimensional subspace, where we derive constraints on the New Physics scale from past and future experiments, illustrating the complementarity of the processes in an intuitive way.