Lepton Flavor Violation from diphoton effective interactions

We consider charged lepton flavor violating transitions mediated by the diphoton effective interactions ${\mathrm{\ell }}_i{\mathrm{\ell }}_j\gamma \gamma$ and explore which processes can probe them better. Our analysis includes single and double radiative decays, ${\mathrm{\ell }}_i\to {\mathrm{\ell }}_j\gamma (\gamma )$, as well as ${\mathrm{\ell }}_i\to {\mathrm{\ell }}_j$ conversions in nuclei for all possible flavor combinations, which we compute for the first time for $\mathrm{\ell }\to \tau$ conversions in this framework. We find that currently the best limits are provided by the loop-induced ${\mathrm{\ell }}_i\to {\mathrm{\ell }}_j\gamma$ processes, while the best future sensitivities come from $\mu \to e$ conversion in aluminum and from potential $\tau \to \mathrm{\ell }\gamma \gamma$ 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.