It was recently suggested that in a class of supersymmetric SO͑10͒ models with Higgs multiplets in 10, and a single 126ϩ126 representation, if the 126 contributes both to the right handed neutrino masses as well as to the charged fermion masses, one can have a complete prediction of the neutrino masses and mixings. It turns out that if one chooses only one 10, there are no regions in the parameter space where one can have a largemixing angle necessary to solve the atmospheric neutrino deficit while at the same time solving the solar neutrino puzzle via the e ↔ oscillation. We show that this problem can be solved in a particular class of SO͑10͒ models with a pair of 10 multiplets if we include the additional left-handed triplet contribution to the light neutrino mass matrix. This model cannot reproduce the mass and mixing parameters required to explain the Liquid Scintillation Neutrino Detector observations nor does it have neutrino hot dark matter. ͓S0556-2821͑98͒01713-5͔ PACS number͑s͒: 12.10. Dm, 12.60.Jv, 14.60.Pq, 26.65.ϩt Strong indications in favor of nonvanishing neutrino masses are emerging from several experiments: ͑i͒ the deficits of solar neutrino flux observed by the four solar neutrino experiments Homestake, Kamiokande, SuperKamiokande, SAGE, and GALLEX ͓1͔ compared to the standard solar model calculations ͓2͔ can be understood if neutrinos are massive and the electron neutrinos emitted by the Sun oscillate to another neutrino species; and ͑ii͒ the atmospheric muon neutrino deficits observed earlier by Kamiokande, IMB, and Soudan II ͓3͔ experiments and confirmed recently by Super Kamiokande can be understood if oscillates similarly. The Liquid Scintillation Neutrino Detector ͑LSND͒ ͓4͔ results have provided the first laboratory indication of ↔ e oscillation and, if confirmed by KARMEN ͓5͔, would seal the case for nonzero neutrino masses, in an unequivocal manner.As is well known, the solar neutrino deficit can be explained in terms of the matter induced resonant Mikheyev-Smirnov-Wolfenstein ͑MSW͒ oscillation ͓6͔ for two choices of masses and mixing angles ͓7͔. Our interest here is in the so-called small angle solution for which ⌬m e 2 Ӎ(0.3Ϫ1.0) ϫ10 Ϫ5 eV 2 and 2ϫ10 Ϫ3 рsin 2 2 e р2ϫ10 Ϫ2 ; The atmospheric neutrino deficit could be due to either ↔ or ↔ e oscillation. Preliminary indications from the electron energy distribution in SuperKamiokande favors ↔ oscillation. Similarly a preliminary fit to all the atmospheric neutrino data ͑sub-GeV, multi-GeV including the zenith angle dependence͒ seems to require 2ϫ10 Ϫ4 рm 2 (eV 2 ) р10 Ϫ2 with sin 2 2 Ӎ0.6Ϫ1.0 ͓8͔. Note the hierarchical pattern of mass differences. The LSND results require that 0.3 eV 2 р⌬m e 2 р10 eV 2 with the mixing angle in the few percent range. If we accept the above results, it is clear that with only three neutrinos, it is not possible to explain the three results ͑i.e., solar, atmospheric, and LSND͒ simultaneously. Therefore within conventional grand unified theories with three generations, one may hope to understand only two ...

We propose a left-right model of quarks and leptons based on the gauge group SU(3)(C)xSU(2)(L)xSU(2)(R)xU(1)(B-L), where the scalar sector consists of only two doublets: (1,2,1,1) and (1,1,2,1). As a result, any fermion mass, whether it be Majorana or Dirac, must come from dimension-five operators. This allows us to have a common view of quark and lepton masses, including the smallness of Majorana neutrino masses as the consequence of a double seesaw mechanism.

The one-loop evolution of couplings in the minimal supersymmetric standard model, extended to include baryon nonconsewing (B) operators through explicit R-parity violation, is considered keeping only B superpotential terms involving the maximum possible number of third generation superfields. If all retained Yukawa couplings Y i are required to remain in the perturbative domain (Y,

The simplest way to simultaneously understand all existing indications of neutrino oscillations from solar and atmospheric neutrino deficits and the LSND experiment, seems to be to postulate a sterile neutrino. We present a realistic grand unified model based on the gauge group SO(10) × SO(10) that leads to the desired masses and mixings for the sterile and the known neutrinos needed to understand the above observations while fitting those of the known charged fermions. The model is a grand unified realization of the recently proposed idea that the sterile neutrino is the lightest neutrino of a mirror sector of the universe which has identical matter and gauge content as the standard model. The two SO(10)'s operate on the two sectors in a mirror symmetric way and are connected by a mixed Higgs representations whose net effect is to connect the superheavy right handed neutrinos of the two sectors.