Flavor-violating dark matter at MEG-II and Mu3e

We investigate the potential of high-intensity muon experiments such as MEG~II and Mu3e to uncover dark matter (DM) through the lepton-flavor-violating decay $\mu^+\to e^+\chi\bar\chi$. We describe the underlying interactions in terms of dimension-six four-fermion operators and systematically explore all allowed Lorentz structures. We show that precision measurements of the Michel spectrum can probe new-physics scales of ${\cal O}({\rm TeV})$ for DM masses above approximately $1~{\rm MeV}$. For lighter DM, whose signal is confined close to the Michel endpoint, the radiative decay $\mu^+\to e^+\chi\bar\chi\gamma$ at MEG~II opens a complementary window, with sensitivity comparable to and, in some regions, stronger than that of the non-radiative channel. Remarkably, for reheating temperatures below the tens-of-MeV scale but above the BBN bound, MEG~II and Mu3e can probe regions in which freeze-in through the very same LFV interactions accounts for the observed DM abundance.