Neutrino pairing as the origin of parity violation in a chiral flavor theory of weak interactions

In this paper we study the space-time and internal-symmetry aspects of weak interactions together with their interplay. We propose that the weak interaction be obtained by gauging the strong-interaction chiral flavor group and consider explicitly the group $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ as a candidate unified gauge theory of weak and electromagnetic interactions. In the symmetry limit the theory is both parity conserving and flavor conserving. The neutrinos in the theory are four-component spinors. We introduce a new dynamical mechanism for obtaining parity violation in weak interactions, namely neutrino pairing, in which we allow pairs of right-handed neutrinos to condense into the vacuum. The group theory associated with this pairing produces maximal parity violation in both the lepton and quark charged-current sectors of the weak interaction and also the conventional Weinberg mixing pattern in the neutral-current sector, while keeping the observed left-handed electron and muon neutrinos massless. In the right-handed sector of the theory, however, the pairing causes the right-handed electron and muon neutrinos to combine into one massive fourcomponent spinor. The unusual phenomenology associated with this new observable massive neutral lepton is studied in detail. Using other representations of the gauge group we also break flavor spontaneously to provide a group-theoretical origin for the Cabibbo angle. Through our approach we can incorporate current algebra and the Gell-Mann-Oakes-Renner Hamiltonian phenomenology into weak-interaction theory. We discuss briefly the implications of our work for constructing grand-unified theories of the strong, electromagnetic, and weak interactions.