$(g-2{)}_{\mathrm{\ell }}$ and LFV decays in a $U(1{)}_{L_{\mu }-L_{\tau }}$ left-right model with inverse seesaw neutrinos

In the framework of a $U(1{)}_{L_{\mu }-L_{\tau }}$ left-right model with inverse seesaw neutrinos recently proposed, we show that one-loop contributions from heavy singly charged Higgs bosons to the anomalous magnetic moments of charged leptons $(g-2{)}_{e,\mu }$ can accommodate the observed discrepancies, of ${10}^{-9}$ and $\mathcal{O}({10}^{-13})$ for the muon and electron, respectively. Meanwhile, all lepton-flavor violating decay rates for $h\to e_b^{\pm }{e}_a^{\mp }$, $Z\to e_b^{\pm }{e}_a^{\mp }$, and $e_b\to e_a\gamma$ are found to be highly suppressed as a consequence of the gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ symmetry.