Flavor violating muon decay into an electron and a light gauge boson

We analyze the flavor violating muon decay $\mu\rightarrow e\chi$, where $\chi$ is a massive gauge boson, with emphasis in the regime where $\chi$ is ultralight. We first study this process from an effective field theory standpoint in terms of form factors. We then present two explicit models where $\mu\rightarrow e\chi$ is generated at tree level and at the one-loop level. We also comment on the prospects of observing the process $\mu\rightarrow e\chi$ in view of the current limits on $\mu\rightarrow 3e$ from the SINDRUM collaboration.