Abstract:
In R parity violating supersymmetry (conserving baryon number B but violating lepton number L), Majorana neutrino masses may arise at tree level, in one loop, and in two loops. The L violating interactions work together with the B + L violating electroweak sphalerons to erase any preexisting B or L asymmetry of the Universe. To have successful leptogenesis nevertheless, a specific scenario is proposed.

Abstract:
Neutrino masses and mixing are generated in a supersymmetric standard model when R-parity is violated in bilinear mass terms. The mixing matrix among the neutrinos takes a restrictive form if the lepton flavor universality holds in the R-parity violating soft masses. It turns out that only the small angle MSW solution to the solar neutrino problem is consistent with the result of the CHOOZ experiment and the atmospheric neutrino data.

Abstract:
We propose an extension of the supersymmetric standard model with right-handed neutrinos and a singlet Higgs field, and study the neutrino masses in this model. The Majorana masses for the right-handed neutrinos are generated around the supersymmetry breaking scale through the vacuum expectation value of the singlet Higgs field. This model may induce spontaneous R-parity violation via the vacuum expectation value of the right-handed sneutrino. In the case, the effective theory is similar to a bilinear R-parity violating model. There are two sources for the neutrino masses: one is this bilinear R-parity breaking effect, and the other is the ordinary seesaw effect between left- and right-handed neutrinos. Combining these two effects, the hierarchical neutrino mass pattern arises even when the neutrino Yukawa matrices are not hierarchical. We acquire appropriate masses and mixings to explain both the solar and atmospheric neutrino oscillations.

Abstract:
In supersymmetric theories, sneutrino--anti-sneutrino mixing can occur with the oscillation time $\sim 0.01$ ps corresponding the atmospheric neutrino mass scale $\sim 0.05$ eV. We explore the possibility of observing sneutrino oscillation phenomena and CP violation when R-parity violation explains the observed neutrino masses and mixing. It is shown for some parameter region in the bilinear model of R-parity violation that the tiny sneutrino mass splitting and time-dependent CP violating asymmetries could be measured in the future experiments if the tau sneutrino is the lightest supersymmetric particle.

Abstract:
In the context of the minimal supersymmetric standard model, nonzero neutrino masses and mixing can be generated through renormalizable lepton number (and thus R-parity) violating operators. It is examined whether neutrino mass matrices from tree and one-loop contributions can account for two mass-squared differences and mixing angles that explain current experimental data. By accommodating, in particular, the solar and atmospheric neutrino data, we find interesting restrictions not only on the free parameters of the theory, such as lepton number violating couplings and soft-parameters, but also on the oscillation parameters of atmospheric neutrinos.

Abstract:
The simplest unified extension of the MSSM with bi-linear R--Parity violation naturally predicts a hierarchical neutrino mass spectrum, in which one neutrino acquires mass by mixing with neutralinos, while the other two get mass radiatively. We have performed a full one-loop calculation of the neutralino-neutrino mass matrix in the bi-linear \rp MSSM, taking special care to achieve a manifestly gauge invariant calculation. Moreover we have performed the renormalization of the heaviest neutrino, needed in order to get meaningful results. The atmospheric mass scale and maximal mixing angle arise from tree-level physics, while solar neutrino scale and oscillations follow from calculable one-loop corrections. If universal supergravity assumptions are made on the soft-supersymmetry breaking terms then the atmospheric scale is calculable as a function of a single \rp violating parameter by the renormalization group evolution due to the non-zero bottom quark Yukawa coupling. The solar neutrino problem must be accounted for by the small mixing angle (SMA) MSW solution. If these assumptions are relaxed then one can implement large mixing angle solutions, either MSW or just-so. The theory predicts the lightest supersymmetic particle (LSP) decay to be observable at high-energy colliders, despite the smallness of neutrino masses indicated by experiment. This provides an independent way to test this solution of the atmospheric and solar neutrino anomalies.

Abstract:
We study extensions of supersymmetric models without R-parity which include an anomalous U(1)_H horizontal symmetry. Bilinear R-parity violating terms induce a neutrino mass at tree level of approximately $(\theta^2)^\delta$ eV where $\theta\approx 0.22$ is the U(1)_H breaking parameter and $\delta$ is an integer number that depends on the horizontal charges of the leptons. For $\delta=1$ a unique self-consistent model arises in which i) all the superpotential trilinear R-parity violating couplings are forbidden by holomorphy; ii) the tree level neutrino mass falls in the range suggested by the atmospheric neutrino problem; iii) radiative contributions to neutrino masses are strongly suppressed resulting in a squared solar mass difference of few 10^{-8} eV^2 which only allows for the LOW (or quasi-vacuum) solution to the solar neutrino problem; iv) the neutrino mixing angles are not suppressed by powers of $\theta$ and can naturally be large.

Abstract:
Neutrino masses and their mixing are studied in detail in the framework of a supersymmetric standard model with bilinear R-parity violation. In this scenario, the mixing matrix among the neutrinos is in a restrictive form. We find that only the small angle MSW solution is allowed for the solar neutrino problem when the results of the CHOOZ experiment are combined with the mass squared difference and mixing angle suggested by the atmospheric neutrino data. Collider signals of this scenario are also discussed.

Abstract:
We discuss general predictions for neutrino masses and mixing angles from R parity violation in the Minimal Supersymmetric Standard Model. If the soft supersymmetry breaking terms are flavor blind at short distance, then the leptonic analogue of the CKM matrix depends on only two real parameters, which are completely determined by fits to solar and atmospheric neutrino oscillations. Either the small angle MSW, large angle MSW, or ``just-so'' solutions to the solar neutrino problem are allowed, although the large angle MSW solution requires substantial fine-tuning. The latter two cases require significant $\nu_\mu\to\nu_e$ oscillations of atmospheric neutrinos. We present a model which could explain bilinear R parity violation as a consequence of spontaneous symmetry violation by a dynamical supersymmetry breaking sector. The decay length and branching ratios of the LSP are estimated.

Abstract:
We analyse a simple RPV extension of the MSSM, with bilinear R-parity violation in the soft terms and vevs, but not between the terms in the superpotential. The model gives two massive neutrinos, and can fit all constraints from neutrino data. We show analytically how to compute the lepton number violating Lagrangian parameters from neutrino masses and mixing angles. Conversely, we numerically vary the bilinear couplings as input parameters to determine the allowed ranges that are consistent with neutrino data. We briefly comment on the implications of our bounds for low energy LFV processes.