Systematic study of leptonic mixing in a class ofSUH(2)models

We perform a systematic analysis of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrices which arise when one assigns the three generations of leptons to the $2\oplus 1$ representation of a horizontal $S{U}_H(2)$ symmetry. This idea was explored previously by Kuchimanchi and Mohapatra. However, we assume (i) the neutrino mass matrix results from leptonic couplings to $S{U}_L(2)$ triplet scalar fields and (ii) hierarchies exist among lepton mass matrix elements which result from couplings to scalar fields with different $S{U}_H(2)$ charges. Of the 16 candidate PMNS matrices which result it is found that only one is both predictive and possesses a leading order structure compatible with experimental data. The relevant neutrino mass matrix displays the symmetry $L_e-L_{\mu }-L_{\tau }$ to leading order and we explore the perturbations required to produce a realistic lepton spectrum. The effective mass in neutrinoless double beta decay is required to lie in the range $⟨m⟩/({10}^{-2}\mathrm{eV})\in [0.7,2.5]$, which is just below current experimental bounds. $U_{e3}$ is nonzero but not uniquely determined.