The question of neutrino mass

We investigate the question of neutrino mass in theories in which neutrinos are four-component Dirac particles. Our analysis is done in the framework of left-right-symmetric theories. The requirement of calculability and natural smallness of neutrino mass leads to the following constraints: (i) left and right charged weak currents must be "orthogonal" to each other, and (ii) there should be no $W_L$-$W_R$ mixing at the tree level. Finally, we exhibit a model in which, due to the existence of an unbroken symmetry of the total Lagrangian, the electron and muon neutrinos remain massless to all orders in perturbation theory.