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

We analyze the flavor violating muon decay $μ\rightarrow eχ$, where $χ$ is a massive gauge boson, with emphasis in the regime where $χ$ 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 $μ\rightarrow eχ$ is generated at tree level and at the one-loop level. We also comment on the prospects of observing the process $μ\rightarrow eχ$ in view of the current limits on $μ\rightarrow 3e$ from the SINDRUM collaboration.