A Three Doublet Lepton-Specific Model

In the lepton-specific version of two Higgs doublet models, a discrete symmetry is used to couple one Higgs, $\Phi_2$, to quarks and the other, $\Phi_1$, to leptons. The symmetry eliminates tree level flavor changing neutral currents (FCNC). Motivated by strong constraints on such currents in the quark sector from meson-antimeson mixing, and by hints of $h \to \mu\tau$ in the lepton sector, we study a simple three Higgs doublet model in which one doublet couples to quarks and the other two to leptons. Unlike most other studies of three Higgs doublet models, we impose no flavor symmetry and just use a $Z_2$ symmetry to constrain the Yukawa couplings. We present the model and discuss the various mixing angles. Constraining the parameters to be consistent with observations of the Higgs boson at the LHC, we study the properties of the charged Higgs boson(s) in the model, focusing on the case in which the charged Higgs is above the top threshold. It is found that one can have the branching fraction of the charged Higgs into $\tau\nu_\tau$ comparable to $t\bar{b}$ decay without needing very large values for the ratios of vevs. One can also get a large branching fraction for the much more easily observable $\mu\nu_\tau$ decay.