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We perform a systematic analysis of the PMNS matrices which arise when oneassigns the three generations of leptons to the $2\oplus 1$ representation of ahorizontal $SU_H(2)$ symmetry. This idea has been previously explored byKuchimanchi and Mohapatra. However, we assume $(i)$ the neutrino mass matrixresults from leptonic couplings to $SU_L(2)$ triplet scalar fields and $(ii)$hierarchies exist amongst lepton mass matrix elements which result fromcouplings to scalar fields with different $SU_H(2)$ charges. Of the sixteencandidate PMNS matrices which result it is found that only one is bothpredictive and possesses a leading order structure compatible with experimentaldata. The relevant neutrino mass matrix displays the symmetry$L_e-L_\mu-L_\tau$ to leading order and we explore the perturbations requiredto produce a realistic lepton spectrum. The effective mass in neutrinolessdouble beta decay is required to lie in the range$<m>/(10^{-2}\mathrm{eV})\in[0.7,2.5]$, which is just below currentexperimental bounds. $U_{e3}$ is non-zero but not uniquely determined.Comment: To appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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