Charged Lepton Flavor Violating Radiative Decays $l_i \to l_j γ$ in G2HDM

Abstract: We compute the electromagnetic form factors of the $l_i l_j \gamma$ vertex at one-loop level in the minimal G2HDM which has a sub-GeV vector dark matter candidate. The results are applied to the radiative decay rates for the charged lepton flavor violating processes $l_i \to l_j \gamma$, and the anomalous magnetic dipole moment and the electric dipole moment of the charged lepton. To numerically compute the branching ratio for $\mu \to e \gamma$ and compare with the latest experimental limit from MEG, we adapt our previous parameter space scan that is consistent with the relic density and constraints from direct searches of dark matter, $W$ and $Z$ mass measurements, as well as the LHC Higgs signal strengths and invisible width. While the extra contributions are at least an order of magnitude smaller than required to explain the $\sim 4.2 \sigma$ discrepancy in the muon anomaly, the existing MEG limit imposes stringent constraint on the parameter space. The remaining viable parameter space can be further probed by the MEG II sensitivity for $\mu \to e \gamma$ as well as from the direct searches of sub-GeV dark matter in foreseeable future. Higher loop contributions may be significant to resolve the discrepancy in the muon anomaly and generate a non-vanishing electric dipole moments for the standard model quarks and leptons in G2HDM.