Neutrinos Are Nearly Dirac Fermions

Abstract

Neutrino masses and mixings are analyzed in terms of left-handed fields and a 6x6 complex symmetric mass matrix whose singular values are the neutrino masses. An angle x_nu characterizes the kind of the neutrinos, with x_nu = 0 for Dirac neutrinos and x_nu = pi/2 for Majorana neutrinos. If x_nu = 0, then baryon-minus-lepton number is conserved. When x_nu is approximately zero, the six neutrino masses coalesce into three nearly degenerate pairs. Thus the smallness of the differences in neutrino masses exhibited in the solar and atmospheric neutrino experiments and the stringent limits on neutrinoless double beta decay are naturally explained if B-L is approximately conserved and neutrinos are nearly Dirac fermions. If one sets sin(x_nu) = 0.003, suppresses inter-generational mixing, and imposes a quark-like mass hierarchy, then one may fit the essential features of the solar, reactor, and atmospheric neutrino experiments with otherwise random mass matrices in the eV range. This B-L model leads to these predictions: neutrinos oscillate mainly between flavor eigenfields and sterile eigenfields, and so the probabilities of the appearance of neutrinos or antineutrinos are very small; neutrinos may well be of cosmological importance; in principle the disappearance of the tau neutrino should be observable; and neutrinoless double beta decay is suppressed by an extra factor of < 10^(-5) and hence will not be seen in the Heidelberg/Moscow, IGEX, GENIUS, or CUORE experiments.