A systematic study of lepton flavor violating dark matter interactions via indirect detection in effective field theories

Lepton flavor violating (LFV) interactions involving dark matter (DM) particles remain a largely unexplored area. In this study, we systematically investigate LFV DM interactions within the framework of effective field theories by analyzing astrophysical photons and positrons produced from DM annihilation. Employing the astrophysical photon and positron data collected by Fermi-LAT, INTEGRAL, XMM-Newton, and AMS-02, we place meaningful constraints on all leading-order effective operators involving a DM pair and a flavor violating charged lepton pair. Our analysis covers the three well-known DM candidates: a scalar, a fermion, and a vector particle. For the photon flux, we consider contributions from final-state radiation, radiative decay, and inverse Compton scattering, and examine their respective sensitivity regions across different DM masses and photon energies. We find that for DM masses below $\mathcal{O}(20\,\rm GeV)$, INTEGRAL provides the most stringent constraints on annihilation cross sections and effective operators in all three LFV channels, whereas AMS-02 offers the strongest constraints above $\mathcal{O}(20\,\rm GeV)$.