Generic Relations of Flavor Mixings between Leptons and Quarks in SU(5)

We have studied implications of the generic lopsided mass matrix of the charged leptons by taking the SU(5) GUT relation in the nearest-neighbor interaction (NNI) basis. We have found four interesting relations among the lepton mixings and the quark ones, which are independent of details of the model. These relations are discussed by using the experimental data. We have also discussed the relation between U_{e2} and U_{e3} incuding the contribution from the neutrino mass matrix. We have presented the probable value U_{e3}=0.05 \sim 0.16, which is independent of the solar neutrino solutions. The CP violating quantity J_{CP} is also discussed.Comment: 16 pages, 2 figures, Some discussions are modified, but results are not change

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA

Phenomenology of Neutrino Mass Matrix

The search for possible mixing patterns of charged leptons and neutrinos is important to get clues of the origin of nearly maximal mixings, since there are some preferred bases of the lepton mass matrices given by underlying theories. We systematically examine the mixing patterns which could lead to large lepton mixing angles. We find out 37 mixing patterns are consistent with experimental data if taking into account phase factors in the mixing matrices. Only 6 patterns of them can explain the observed data without any tuning of parameters, while the others need particular choices for phase values.Comment: revised reference

Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?

We investigate whether the lepton flavor mixing angles in the so-called democratic type of mass matrix are stable against quantum corrections or not in the minimal supersymmetric standard model with dimension five operator which induces neutrino mass matrix. By taking simple breaking patterns of $S_3{}_L \times S_3{}_R$ or $O(3)_L \times O(3)_R$ flavor symmetries and the scale where democratic textures are induced as $O(10^{13})$ GeV, we find that the stability of the lepton flavor mixing angles in the democratic type of mass matrix against quantum corrections depends on the solar neutrino solutions. The maximal flavor mixing of the vacuum oscillation solution is spoiled by the quantum corrections in the experimental allowed region of $\tan \beta$. The large angle MSW solution is spoiled by the quantum corrections in the region of $\tan \beta > 10$. The condition of $\tan \beta \leq 10$ is needed in order to obtain the suitable mass squared difference of the small angle MSW solution. These strong constraints must be regarded for the model building of the democratic type of mass matrixComment: 12pages,LaTe

Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as $M_A^3$, are studied. The total spacetime is of the form $M^4\times M_A^3$. The range of the Sol corrections is investigated and compared to the range of the $T^3$ corrections.Comment: 13 pages, 10 figures, published versio

What Does mu-tau Symmetry Imply about Neutrino Mixings?

The requirement of the mu-tau symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin(\theta_{13})=0 (referred to as C1)) or sin(\theta_{12})=0 (referred to as C2)), where \theta_{12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately mu-tau symmetric textures. It is argued that the tiny mu-tau symmetry breaking generally leads to cos(2\theta_{23}) \simsin(\theta_{13}) for C1) and cos(2\theta_{23}) \sim \Delta m^2_\odot/\Delta m^2_{atm}(\equiv R) for C2), which indicates that the smallness of cos(2\theta_{23}) is a good measure of the mu-tau symmetry breaking, where \Delta m^2_{atm} (\Delta m^2_\odot) stands for the square mass differences of atmospheric (solar) neutrinos. We further find that the relation R \sim sin^2(\theta_{13}) arises from contributions of O(sin^2(\theta_{13})) in the estimation of the neutrino masses (m_{1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin^2(2\theta_{12})=O(1) for C2). To satisfy R \sim sin^2(\theta_{13}) for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}| \sim O(\sqrt{\Delta m^2_{atm}}), and, to realize sin^2(2\theta_{12})=O(1) for C2), there should be an additional small parameter \eta whose size is comparable to that of the mu-tau symmetry breaking parameter \epsilon, giving tan(2\theta_{12}) \sim \epsilon/\eta with \eta \sim \epsilon to be compatible with the observed large mixing.Comment: 10 pages, title slightly modified, comments added in the introdction, typos corrected, references updated, version to appear in Physical Reviews