Lepton Flavor Violation in SUSY GUT Model with Non-universal Sfermion Masses

We analyze lepton flavor violating $\tau \to \mu \gamma$ and $\mu \to e \gamma$ processes in SUSY GUT model in which sfermions have special mass spectrum. It is assumed that only third generation sfermions which are contained in ${\bf 10}(Q, U^c, E^c)$ of SU(5) can have a different mass from the others. This mass spectrum is led from $E_6$ GUT model with horizontal symmetries. It is shown that branching ratios of $\tau \to \mu \gamma$ and $\mu \to e \gamma$ depend strongly on a right-handed stau mass. The weak scale stability requires the light stau, so large decay rates can be expected in this scenario. When stau is around 150 GeV and $\tan \beta \sim 10$, the branching ratios can be larger than $Br(\tau \to \mu \gamma) \simeq 10^{-8}$ and $Br(\mu \to e \gamma) \simeq 5\times 10^{-12}$, which are within reach of future experiments. In addition, this model has an interesting feature that the final state charged lepton tends to have the right-handed chirality.Comment: 17 pages, 12 figures, v3 a reference adde

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Determining the Neutrino Mass Hierarchy with Atmospheric Neutrinos

The possibility to determine the type of neutrino mass hierarchy by studying atmospheric neutrino oscillations with a detector capable to distinguish between neutrino and antineutrino events, such as magnetized iron calorimeters, is considered. We discuss how the ability to distinguish between the neutrino mass spectrum with normal and inverted hierarchy depends on detector characteristics like neutrino energy and direction resolutions or charge miss-identification, and on the systematical uncertainties related to the atmospheric neutrino fluxes. We show also how the neutrino mass hierarchy determination depends on the true values of $\theta_{13}$ and $\theta_{23}$, as well as on the type of the true hierarchy. We find that for $\mu$-like events, an accurate reconstruction of the energy and direction of the neutrino greatly improves the sensitivity to the type of neutrino mass spectrum. For $\sin^22\theta_{13} \cong 0.1$ and a precision of 5% in the reconstruction of the neutrino energy and $5^\circ$ in the neutrino direction, the type of neutrino mass hierarchy can be identified at the 2$\sigma$ C.L. with approximately 200 events. For resolutions of 15% for the neutrino energy and $15^\circ$ for the neutrino direction roughly one order of magnitude larger event numbers are required. For a detector capable to distinguish between $\nu_e$ and $\bar\nu_e$ induced events the requirements on energy and direction resolutions are, in general, less demanding than for a detector with muon charge identification.Comment: 24 pages, 8 figure

Critical behavior of an Ising model with aperiodic interactions

We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, the uniform fixed point in the parameter space becomes fully unstable. We analyze some limiting cases, and propose a heuristic criterion to check the relevance of the fluctuations.Comment: latex file, 5 figures, accepted by Braz. Jour. Phy