LFV decays in a 3-4-1 model with minimal inverse seesaw neutrinos

We investigate an extended 3-4-1 model consisting of a new singly charged Higgs boson, implementing the minimal inverse seesaw mechanism to accommodate the large values of the $(g-2{)}_{e,\mu }$ anomalies as well as the lepton-flavor-violating decay rates of charged leptons, the Standard Model-like Higgs boson, and the $Z$ boson, all consistent with current experimental data. Unlike the previously studied 3-4-1 realization, the model considered here predicts strong correlations among these observables that can be tested in future experiments. In particular, the current upper bound on Br$(\tau \to \mu \gamma )$ imposes a stringent constraint compatible with the $1\sigma$ experimental range of $(g-2{)}_{\mu }$, corresponding to a maximal deviation of ${10}^{-9}$ from the SM prediction. The forthcoming experimental sensitivity to Br$(\tau \to \mu \gamma )$ will reduce this deviation to $5\times {10}^{-10}$.