Neutrino Masses, Lepton Number Violation and Unification

Abstract

Among the energy scales of elementary particle physics, the following quantities are compatible with being zero: the graviton, the gluon and photon masses, the electron’s decay width Γ_e, the proton’s decay width Γ_p, and, finally, the neutrino masses m_ν. Whereas we have a dynamical understanding of the vanishing of the first four in terms of suitable gauge principles, Γ_e = 0 being guaranteed by electric charge conservation, the same is apparently not true for the vanishing (or the smallness) of Γ_p and m_ν. In fact, the supposedly conserved relevant quantities, baryon and lepton numbers, could not possibly correspond to unbroken local symmetries*. For a believer in the currently fashionable Gauge Symmetry Dogma, i.e., that exact symmetries in Nature are local ones, this is enough to want Γ_p and m_ν to be different from zero. Now, of course, the very important recent work on baryon creation in the Universe gives also, for the first time, a good “experimental” reason for the proton to decay. It seems therefore worth while to give a discussion of the possible generation of neutrino masses. This is what I shall do in this talk, trying to keep the various arguments on general grounds, rather than going into model dependent details.