Abstract
We propose a model having a gauged SU(2) symmetry associated with the second and third generations of leptons, dubbed SU(2)μτ, of which mathrm{U}{(1)}_{{mathbb{L}}_{mu }-{mathbb{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)μτ doublet and SM singlet that develops a nonzero vacuum expectation value at presumably multi-TeV scale to completely break the SU(2)μτ symmetry, rendering three massive gauge bosons. At the same time, the other exotic scalar field, carrying electroweak as well as SU(2)μτ 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.
Highlights
After symmetry breaking induced by the vacuum expectation value (VEV) of a scalar SU(2)μτ doublet, the gauged flavor group has three massive gauge bosons, denoted by X3,±, with X3 corresponding to the U(1)Lμ−Lτ subgroup and X± coupled with currents that exchange the muon and tau numbers by one unit
To break the mass degeneracy between μ and τ as otherwise required by the new flavor symmetry, we further introduce a set of scalar fields that transform as a triplet under SU(2)μτ and a doublet under the Standard Model (SM) SU(2)L
To break the SU(2)μτ symmetry, we introduce a scalar field S, which is a singlet under the SM gauge group and a doublet under the gauge flavor symmetry
Summary
The Michel decays of the tau lepton can be modified by both X± and H± bosons at tree level. We note in passing that if MX /gX and M are comparable and all X±, h±, and H± can contribute to the muon g − 2 and the Michel decays of τ leptons, it is possible to find some more allowed parameter space in the (MX , gX ) plane and the (M, tan β) plane. To see this cooperative effect clearly, we make plots in the (M, MX ) plane for fixed (gX , α ) in figure 6 for several values of tan β. A comparison among the three plots indicates that MX needs to be greater than a few tens of GeV and that more parameter space is allowed for larger tan β
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