Neutrino Mass and Spontaneous Parity Nonconservation

In weak-interaction models with spontaneous parity nonconservation, based on the gauge group $\mathrm{SU}{(2)}_{L}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{R}\ensuremath{\bigotimes}\mathrm{U}(1)$, we obtain the following formula for the neutrino mass: ${m}_{{\ensuremath{\nu}}_{e}}\ensuremath{\simeq}\frac{{{m}_{e}}^{2}}{g{m}_{{W}_{R}}}$, where ${W}_{R}$ is the gauge boson which mediates right-handed weak interactions. This formula, valid for each lepton generation, relates the maximality of observed parity nonconservation at low energies to the smallness of neutrino masses.

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