Abstract:
There are several indications that the Majorana masses of the right-handed neutrino components, $M_R,$ are at the intermediate scale: $M_R\sim (10^{10}-10^{12})$ GeV or even lighter. The renormalization effects due to large Yukawa couplings of neutrinos from region of momenta $M_R \ltap q \ltap M_G$ are studied in the supersymmetric standard model. It is shown that neutrino renormalization effect can increase the $m_b/m_\tau$ ratio up to $(10\div 15)\%.$ This strongly disfavours $m_b-m_\tau$ unification for low values of $\tan\beta < 10$ especially at large values of $\alpha_s.$ Lower bounds on $M_R$ and $\tan\beta$ from the $b-\tau$ unification condition were found. The implications of the results to the see-saw mechanism of the neutrino mass generation are discussed.

Abstract:
We investigate the possibility of accommodating neutrino masses compatible with the MSW study of the Solar neutrino deficit within the minimal supersymmetric Standard Model. The ``gravity-induced'' seesaw mechanism based on an interplay of nonrenormalizable and renormalizable terms in the superpotential allows neutrino masses $m_\nu\propto m_u^2/M_I$, with $m_u$ the corresponding quark mass and $M_I\simeq 4\times10^{11}$ GeV, while at the same time ensuring the grand desert with the gauge coupling unification at $M_U\simeq 2\times10^{16}$ GeV. The proposed scenario may be realized in a class of string vacua, {\it i.e.,} large radius ($R^2/\alpha '={\cal O}(20)$) $(0,2)$ Calabi-Yau spaces. In this case $M_U^2=M_C^2/{\cal O} (2R^2/\alpha')$ and $M_I= {\cal O}(e^{-R^2/\alpha'})M_C$. Here $M_C=g\times 5.2\times 10^{17}$GeV is the scale of the tree level (genus zero) gauge coupling ($g$) unification.

Abstract:
We present a ``gravity-induced'' seesaw mechanism, which accommodates neutrino masses ($m_\nu\propto m_u^2/M_I$, with $m_u$ the corresponding quark mass and $M_I\simeq 4\times10^{11}$ GeV) compatible with the MSW study of the Solar neutrino deficit within the minimal supersymmetric Standard Model (the grand desert with the gauge coupling unification at $M_U\simeq 2\times10^{16}$ GeV). We show that for large radius ($R^2/\alpha '={\cal O}(20)$) Calabi-Yau spaces, threshold corrections ensure $M_U^2=M_C^2/{\cal O} (2R^2/\alpha')$ and the magnitude of the non-renormalizable terms in the superpotential yields $M_I= {\cal O}(e^{-R^2/\alpha'})M_C$. Here $M_C=g\times 5.2\times 10^{17}$GeV is the scale of the tree level (genus zero) gauge coupling ($g$) unification.

Abstract:
We provide, in the R-parity violating supersymmetric standard model, a comprehensive analysis for sneutrino minimization from the one-loop effective scalar potential, and also for one-loop renormalized neutrino masses and mixing by calculating the effective neutrino mass matrix in the weak basis. Applying our results to theories with gauge mediated supersymmetry breaking, we show how atmospheric and solar neutrino oscillations can be accommodated simultaneously in this framework. It is observed that the one-loop correction to sneutrino vacuum expectation values leads to a significant effect on the determination of the neutrino masses and mixing.

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:
The generic supersymmetric standard model is a model built from a supersymmetrized standard model field spectrum the gauge symmetries only. The popular minimal supersymmetric standard model differs from the generic version in having R-parity imposed by hand. We review an efficient formulation of the model in which all the admissible R-parity violating terms are incorporated without bias. The model gives many new interesting R-parity violating phenomenological features only started to be studied recently. Some of our recent results will be discussed, including newly identified 1-loop contributions to neutrino masses and electric dipole moments of neutron and electron. This is related to the largely overlooked R-parity violating contributions to squark and slepton mixings, which we also present in detail.

Abstract:
In the minimal standard electroweak gauge model, there is an effective dimension-five operator which generates neutrino masses, and it has only three tree-level realizations. One is the canonical seesaw mechanism with a right-handed neutrino. Another is having a heavy Higgs triplet as recently proposed. The third is to have a heavy Majorana fermion triplet, an example of which is presented here in the context of supersymmetric SU(5) grand unification. The three generic one-loop realizations of this operator are also discussed.

Abstract:
We examine the lepton-flavor violation caused by a Yukawa coupling matrix $y_{\nu,ij}$ for right-handed neutrinos in the supersymmetric standard model. We stress that decay rates for $\tau\rightarrow\mu\gamma$ and $\mu\rightarrow e\gamma$ may reach the range to be accessible to near future experiments if left-right mixing terms in the slepton mass matrix are substantially large.

Abstract:
R-parity-violating supersymmetry with a conserved baryon number B provides a framework for particle physics with lepton number (L) violating interactions. Two important probes of the L-violating physics are neutrino masses and sneutrino-antisneutrino mass-splittings. We evaluate these quantities in the context of the most general CP-conserving, R-parity-violating B-conserving extension of the minimal supersymmetric standard model. In generic three-generation models, three sneutrino-antisneutrino mass splittings are generated at tree-level. In contrast, only one neutrino mass is generated at tree-level; the other two neutrinos acquire masses at one-loop. In many models, the dominant contribution to the radiative neutrino masses is induced by the non-zero sneutrino-antisneutrino mass splitting.