Atmospheric and Solar Neutrino Oscillations in \nuMSSM and Beyond

We show how a unified description of the various two-flavor neutrino oscillation solutions, allowed by the atmospheric and solar neutrino experiments, are naturally realized within the framework of $\nu$MSSM (MSSM augmented with the seesaw mechanism) and beyond, especially grand unified theories. A general mechanism for achieving maximal mixing to resolve the atmospheric anomaly is discussed, and applied to the flipped SU(5) model. Except in the case of MSSM and SU(5), a light sterile neutrino is an inevitable consequence of our considerations. The bi-maximal neutrino mixing scenario is one of the options considered. Neutrino hot dark matter can arise in models with maximal $\nu_{\mu}-\nu_s$ oscillations. A ${\cal U}(1)$ flavor symmetry, motivated by the charged fermion mass hierarchies and the magnitudes of the CKM matrix elements, plays a central role.Comment: 14 pp, LATEX. Typos are corrected, possibilities of the neutrino HDM in various scenarios are emphasize

An Improved Supersymmetric SU(5)

By supplementing minimal supersymmetric SU(5) (MSSU(5)) with a flavor ${\cal U}(1)$ symmetry and two pairs of $\bar{15}+15$ `matter' supermultiplets, we present an improved model which explains the charged fermion mass hierarchies and the magnitudes of the CKM matrix elements, while avoiding the undesirable asymptotic mass relations $m_s=m_{\mu}, m_d/m_s = m_e/m_{\mu}$. The strong coupling $\alpha_s (M_Z)$ is predicted to be approximately 0.115, and the proton lifetime is estimated to be about five times larger than the MSSU(5) value. The atmospheric and solar neutrino puzzles are respectively resolved via maximal $\nu_{\mu}-\nu_{\tau}$ and small mixing angle $\nu_e-\nu_s$ MSW oscillations, where $\nu_s$ denotes a sterile neutrino. The ${\cal U}(1)$ symmetry ensures not only a light $\nu_s$ but also automatic `matter' parity.Comment: 11 pp. LATEX. Version with minor addition accepted for publication in Physics Letters

Bi-maximal Neutrino Mixings And Proton Decay In SO(10) With Anomalous Flavor U(1){\cal U}(1)

By supplementing supersymmetric SO(10) with an anomalous ${\cal U}(1)$ flavor symmetry and additional `matter' superfields carrying suitable ${\cal U}(1)$ charges, we explain the charged fermion mass hierarchies, the magnitudes of the CKM matrix elements, as well as the solar and atmospheric neutrino data. We stress bi-maximal vacuum neutrino mixings, and indicate how the small or large mixing angle MSW solution can be incorporated. The ${\cal U}(1)$ symmetry also implies that $\tau_{p\to K\nu}[SO(10)]\sim (10-100)\cdot \tau_{p\to K\nu}[{\rm minimal}~SU(5)]$.Comment: 4 pages, revte

Coannihilation Scenarios and Particle Spectroscopy in SU(4)_c x SU(2)_L x SU(2)_R

We identify a variety of coannihilation scenarios in a supersymmetric SU(4)_c x SU(2)_L x SU(2)_R model with discrete left-right symmetry. Non-universal gaugino masses, compatible with the gauge symmetry, play an essential role in realizing gluino and bino-wino coannihilation regions that are consistent with the WMAP dark matter constraints. We also explore regions of the parameter space in which the little hierarchy problem is partially resolved. We present several phenomenologically interesting benchmark points and the associated sparticle and Higgs mass spectra.Comment: 16 pages, 5 figures and 1 tabl

Guaranteeing Spatial Uniformity in Diffusively-Coupled Systems

We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components has its own weighted undirected graph describing the topology of the interconnection between compartments. The condition makes use of the Jacobian matrix to describe the dynamics of each compartment as well as the Laplacian eigenvalues of each of the graphs. We discuss linear matrix inequalities that can be used to verify the condition guaranteeing spatial uniformity, and apply the result to a coupled oscillator network. Next we turn to reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous condition guaranteeing spatial uniformity of solutions. The paper contributes a relaxed condition to check spatial uniformity that allows individual components to have their own specific diffusion terms and interconnection structures

Flavor Problem, Proton Decay And Neutrino Oscillations In SUSY Models With Anomalous U(1){\cal U}(1)

We discuss how realistic supersymmetric models can be constructed by employing an anomalous ${\cal U}(1)$ flavor symmetry which also mediates supersymmetry breaking. A judicious choice of ${\cal U}(1)$ charges enables the first two squark families to be sufficiently heavy ($\stackrel{>}{_\sim}10$ TeV), so that flavor changing neutral currents as well as dimension five nucleon decay are adequately suppressed. Using the SU(5) example, the charged fermion mass hierarchies, magnitudes of the CKM matrix elements, as well as the observed neutrino oscillations are simultaneously accommodated. We estimate the proton lifetime to be $\tau_p\sim 10^3\cdot \tau_p[{\rm minimal} SU(5)]$, with the decay mode $p\to K\mu$ being comparable to $p\to K\nu_{\mu, \tau}$.Comment: Additional references included. Version to appear in Phys. Lett.

Gravity Waves and Gravitino Dark Matter in μ\mu-Hybrid Inflation

We propose a novel reformulation of supersymmetric (more precisely $\mu$-) hybrid inflation based on a local U(1) or any suitable extension of the minimal supersymmetric standard model (MSSM) which also resolves the $\mu$ problem. We employ a suitable Kahler potential which effectively yields quartic inflation with non-minimal coupling to gravity. Imposing the gravitino Big Bang Nucleosynthesis (BBN) constraint on the reheat temperature ($T_r \lesssim 10^6$ GeV) and requiring a neutralino LSP, the tensor to scalar ratio ($r$) has a lower bound $r \gtrsim 0.004$. The U(1) symmetry breaking scale lies between $10^8$ and $10^{12}$ GeV. We also discuss a scenario with gravitino dark matter whose mass is a few GeV.Comment: 5 pages, 4 figures, revised version to appear in Physics Letters

\theta_13, Rare Processes and Proton Decay in Flipped SU(5)

We consider an extended flipped SU(5) model, supplemented by a flavor ${\cal U}(1)$ symmetry, which yields bi-large neutrino mixings, charged fermion mass hierarchies and CKM mixings. The third leptonic mixing angle \te_{13} turns out to lie close to 0.07, and neutrino CP violation can be estimated from the observed baryon asymmetry. For lepton flavor violating processes we find the branching ratios, {\rm BR}(\mu \to e\ga)\sim {\rm BR}(\tau \to e \ga) \sim 10^{-4}\cdot {\rm BR}(\tau \to \mu \ga) \stackrel{<}{_\sim}5\cdot 10^{-14}. The proton lifetime $\tau_{p\to \pi^0 e^{+}}\simeq 10^{34}-10^{36}$ yrs.Comment: Discussion on leptogenesis and CP violation, and references adde