Alternatives to the seesaw mechanism are explored in supersymmetric models with three right-handed or sterile neutrinos. Tree-level Yukawa couplings can be drastically suppressed in a natural way to give sub-eV Dirac neutrino masses. If, in addition, a B-L gauge symmetry broken at a large scale MG is introduced, a wider range of possibilities opens up. The value of the right-handed neutrino mass MR can be easily disentangled from that of MG. Dirac and Majorana neutrino masses at the eV scale can be generated radiatively through the exchange of sneutrinos and neutralinos. Dirac masses mD owe their smallness to the pattern of light-heavy scales in the neutralino mass matrix. The smallness of the Majorana masses mL is linked to a similar seesaw pattern in the sneutrino mass matrix. Two distinct scenarios emerge. In the first, with very small or vanishing MR, the physical neutrino eigenstates are, for each generation, either two light Majorana states with a mixing angle ranging from very small to maximal, depending on the ratio mD/MR, or one light Dirac state. In the second scenario, with a large value of MR, the physical eigenstates are two nearly unmixed Majorana states with masses ∼mL and ∼MR. In both cases, the (B-L)-breaking scale MG is, in general, much smaller than that in the traditional seesaw mechanism.
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