Neutrino masses and mixings in gauge models with spontaneous parity violation

Unified electroweak gauge theories based on the gauge group $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{B-L}$, in which the breakdown of parity invariance is spontaneous, lead most naturally to a massive neutrino. Assuming the neutrino to be a Majorana particle, we show that smallness of its mass can be understood as a result of the observed maximality of parity violation in low-energy weak interactions. This result is shown to be independent of the number of generations and unaffected by renormalization effects. Phenomenological consequences of this model at low energies are studied. Observation of neutrinoless double-$\beta$ decay will provide a crucial test of this class of models. Implications for rare decays such as $\mu \to e\gamma$, $\mu \to \mathrm{ee}\overline{e}$, etc. are also noted. It is pointed out that in the realm of neutral-current phenomena, departure from the predictions of the standard model for polarized-electron-hadron scattering, forward-backward asymmetry in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, and neutrino interactions has a universal character and may be therefore used as a test of the model.