Model with a gauged lepton flavor SU(2) symmetry

We propose a model having a gauged $SU(2)$ symmetry associated with the second and third generations of leptons, dubbed $SU(2{)}_{\mu \tau }$, of which $U(1{)}_{L_{\mu }-L_{\tau }}$ is an Abelian subgroup. In addition to the Standard Model fields, we introduce two types of scalar fields. One exotic scalar field is an $SU(2{)}_{\mu \tau }$ doublet and SM singlet that develops a nonzero vacuum expectation value at presumably multi-TeV scale to completely break the $SU(2{)}_{\mu \tau }$ symmetry, rendering three massive gauge bosons. At the same time, the other exotic scalar field, carrying electroweak as well as $SU(2{)}_{\mu \tau }$ charges, is induced to have a nonzero vacuum expectation value as well and breaks mass degeneracy between the muon and tau. We examine how the new particles in the model contribute to the muon anomalous magnetic moment in the parameter space compliant with the Michel decays of tau.