A Supersymmetric Contribution to the Neutrino Mass Matrix and Breaking of mu-tau Symmetry

Supersymmetry broken by anomaly mediation suffers from tachyonic slepton masses. A possible solution to this problem results in "decoupling", i.e., the first two generations of sfermions are much heavier than the third one. We note that in this scenario a sizable loop-induced contribution to the neutrino mass matrix results. As an application of this scenario we take advantage of the fact that the decoupling evidently not obeys 2-3 generation exchange symmetry. In the neutrino sector, this 2-3 symmetry (or mu-tau symmetry) is a useful Ansatz to generate zero theta_{13} and maximal theta_{23}. The induced deviations from these values are given for some examples, thereby linking SUSY breaking to the small parameters (including possibly the solar mass splitting) of the neutrino sector.Comment: 5 pages, 1 figur

(S)fermion Masses in Fat Brane Scenario

We discuss the fermion mass hierarchy and the flavor mixings in the fat brane scenario of a five dimensional SUSY theory. Assuming that the matter fields lives in the bulk, their zero mode wave functions are Gaussians, and Higgs fields are localized on the brane, we find simple various types of the matter configurations generating the mass matrices consistent with experimental data. Sfermion mass spectrum is also discussed using the matter configurations found above. Which type of squark mass spectra (the degeneracy, the decoupling and the alignment) is realized depends on the relative locations of SUSY breaking brane and the brane where Higgs fields are localized.Comment: 18 pages, LaTe

Relativistic diffusion with friction on a pseudoriemannian manifold

We study a relativistic diffusion equation on the Riemannian phase space defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin) differential equations (defining the diffusion) as a perturbation by noise of the geodesic equation. We show that the expectation value of the angular momentum and the energy grow exponentially fast. We discuss drifts leading to an equilibrium. It is shown that the diffusion process corresponding to the Juettner or quantum equilibrium distributions has a bounded expectation value of angular momentum and energy. The energy and the angular momentum tend exponentially fast to their equilibrium values. As examples we discuss a particle in a plane fronted gravitational wave and a particle in de Sitter universe. It is shown that the relativistic diffusion of momentum in de Sitter space is the same as the relativistic diffusion on the Minkowski mass-shell with the temperature proportional to the de Sitter radius.Comment: the version published in CQ

Gauge-Fermion Unification and Flavour Symmetry

After we study the 6-dimensional ${\cal N} = (1, 1)$ supersymmetry breaking and $R$ symmetry breaking on $M^4\times T^2/Z_n$, we construct two ${\cal N} = (1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_3$ where $E_6$ is broken down to $SO(10)\times U(1)_X$ by orbifold projection. In Model I, three families of the Standard Model fermions arise from the zero modes of bulk vector multiplet, and the $R$ symmetry $U(1)_F^{I} \times SU(2)_{{\bf 4}_-}$ can be considered as flavour symmetry. This may explain why there are three families of fermions in the nature. In Model II, the first two families come from the zero modes of bulk vector multiplet, and the flavour symmetry is similar. In these models, the anomalies can be cancelled, and we have very good fits to the SM fermion masses and mixings. We also comment on the ${\cal N}=(1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_4$ and $M^4\times T^2/Z_6$, SU(9) models on $M^4\times T^2/Z_3$, and SU(8) models on $T^2$ orbifolds.Comment: Latex, 33 pages, minor change

Relativistic diffusive motion in random electromagnetic fields

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).Comment: the version published in JP

Gauge-Higgs Dark Matter

When the anti-periodic boundary condition is imposed for a bulk field in extradimensional theories, independently of the background metric, the lightest component in the anti-periodic field becomes stable and hence a good candidate for the dark matter in the effective 4D theory due to the remaining accidental discrete symmetry. Noting that in the gauge-Higgs unification scenario, introduction of anti-periodic fermions is well-motivated by a phenomenological reason, we investigate dark matter physics in the scenario. As an example, we consider a five-dimensional SO(5)\timesU(1)_X gauge-Higgs unification model compactified on the $S^1/Z_2$ with the warped metric. Due to the structure of the gauge-Higgs unification, interactions between the dark matter particle and the Standard Model particles are largely controlled by the gauge symmetry, and hence the model has a strong predictive power for the dark matter physics. Evaluating the dark matter relic abundance, we identify a parameter region consistent with the current observations. Furthermore, we calculate the elastic scattering cross section between the dark matter particle and nucleon and find that a part of the parameter region is already excluded by the current experimental results for the direct dark matter search and most of the region will be explored in future experiments.Comment: 16 pages, 2 figure

Exploring the neutrino mass matrix at M_R scale

We discuss the neutrino mass matrix which predicts zero or small values of |V_{13}| in MSSM and found the inequality, sin^2 2theta_{12} <= sin^2 2theta_sol, where sin^2 2theta_{12} is the mixing angle at M_R scale and sin^2 2theta_{sol} is the value determined by the solar neutrino oscillation. This constraint says that the model which predicts a larger value of tan^2 theta_{sol} at M_R than the experimental value is excluded. In particular, the bi-maximal mixing scheme at M_R scale is excluded, from the experimental value tan^2 theta_sol<1. In this model, |V_{13}| and a Dirac phase at m_Z are induced radiatively and turn out to be not small. The effective neutrino mass is expected to be of order 0.05 eV.Comment: revtex4, 20 pages, 6 figure

Rings Reconcile Genotypic and Phenotypic Evolution within the Proteobacteria.

Although prokaryotes are usually classified using molecular phylogenies instead of phenotypes after the advent of gene sequencing, neither of these methods is satisfactory because the phenotypes cannot explain the molecular trees and the trees do not fit the phenotypes. This scientific crisis still exists and the profound disconnection between these two pillars of evolutionary biology--genotypes and phenotypes--grows larger. We use rings and a genomic form of goods thinking to resolve this conundrum (McInerney JO, Cummins C, Haggerty L. 2011. Goods thinking vs. tree thinking. Mobile Genet Elements. 1:304-308; Nelson-Sathi S, et al. 2015. Origins of major archaeal clades correspond to gene acquisitions from bacteria. Nature 517:77-80). The Proteobacteria is the most speciose prokaryotic phylum known. It is an ideal phylogenetic model for reconstructing Earth's evolutionary history. It contains diverse free living, pathogenic, photosynthetic, sulfur metabolizing, and symbiotic species. Due to its large number of species (Whitman WB, Coleman DC, Wiebe WJ. 1998. Prokaryotes: the unseen majority. Proc Nat Acad Sci U S A. 95:6578-6583) it was initially expected to provide strong phylogenetic support for a proteobacterial tree of life. But despite its many species, sequence-based tree analyses are unable to resolve its topology. Here we develop new rooted ring analyses and study proteobacterial evolution. Using protein family data and new genome-based outgroup rooting procedures, we reconstruct the complex evolutionary history of the proteobacterial rings (combinations of tree-like divergences and endosymbiotic-like convergences). We identify and map the origins of major gene flows within the rooted proteobacterial rings (P &lt; 3.6 × 10(-6)) and find that the evolution of the "Alpha-," "Beta-," and "Gammaproteobacteria" is represented by a unique set of rings. Using new techniques presented here we also root these rings using outgroups. We also map the independent flows of genes involved in DNA-, RNA-, ATP-, and membrane- related processes within the Proteobacteria and thereby demonstrate that these large gene flows are consistent with endosymbioses (P &lt; 3.6 × 10(-9)). Our analyses illustrate what it means to find that a gene is present, or absent, within a gene flow, and thereby clarify the origin of the apparent conflicts between genotypes and phenotypes. Here we identify the gene flows that introduced photosynthesis into the Alpha-, Beta-, and Gammaproteobacteria from the common ancestor of the Actinobacteria and the Firmicutes. Our results also explain why rooted rings, unlike trees, are consistent with the observed genotypic and phenotypic relationships observed among the various proteobacterial classes. We find that ring phylogenies can explain the genotypes and the phenotypes of biological processes within large and complex groups like the Proteobacteria

Green functions and propagation of waves in strongly inhomogeneous media

We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium

Democratic Neutrino Mixing and Radiative Corrections

The renormalization effect on a specific ansatz of lepton mass matrices, arising naturally from the breaking of flavor democracy for charged leptons and that of mass degeneracy for light neutrinos, is studied from a superhigh energy scale M_0 \sim 10^{13} GeV to the electroweak scale in the framework of the minimal supersymmetric standard model. We find that the democratic neutrino mixing pattern obtained from this ansatz may in general be instable against radiative corrections. With the help of similar flavor symmetries we prescribe a slightly different scheme of lepton mass matrices at the scale M_0, from which the democratic mixing pattern of lepton flavors can be achieved, after radiative corrections, at the experimentally accessible scales.Comment: RevTex 8 pages. Phys. Rev. D (in printing