Lepton Flavor Violation from diphoton effective interactions

We consider charged lepton flavor violating transitions mediated by the diphoton effective interactions $\ell_i\ell_j\gamma\gamma$ and explore which processes can probe them better. Our analysis includes single and double radiative decays, $\ell_i\to\ell_j\gamma(\gamma)$, as well as $\ell_i\to\ell_j$ conversions in nuclei for all possible flavor combinations, which we compute for the first time for $\ell\to\tau$ conversions in this framework. We find that currently the best limits are provided by the loop-induced $\ell_i\to\ell_j\gamma$ processes, while the best future sensitivities come from $\mu\to e$ conversion in aluminum and from potential $\tau\to \ell\gamma\gamma$ searches at Belle II or at the Super Tau Charm Facility. We also motivate the search for $\mu\to e\gamma\gamma$ at the Mu3e experiment as a complementary probe of these operators.