Theoretical Constraints on the Vacuum Oscillation Solution to the Solar Neutrino Problem

The vacuum oscillation (VO) solution to the solar anomaly requires an extremely small neutrino mass splitting, Delta m^2_{sol}\leq 10^{-10} eV^2. We study under which circumstances this small splitting (whatever its origin) is or is not spoiled by radiative corrections. The results depend dramatically on the type of neutrino spectrum. If m_1^2 \sim m_2^2 \geq m_3^2, radiative corrections always induce too large mass splittings. Moreover, if m_1 and m_2 have equal signs, the solar mixing angle is driven by the renormalization group evolution to very small values, incompatible with the VO scenario (however, the results could be consistent with the small-angle MSW scenario). If m_1 and m_2 have opposite signs, the results are analogous, except for some small (though interesting) windows in which the VO solution may be natural with moderate fine-tuning. Finally, for a hierarchical spectrum of neutrinos, m_1^2 << m_2^2 << m_3^2, radiative corrections are not dangerous, and therefore this scenario is the only plausible one for the VO solution.Comment: 13 pages, LaTeX, 3 ps figures (psfig.sty

Model Independent Electromagnetic corrections in hadronic τ\tau decays

The long distance correction to the total decay width of the $\tau^{\pm}\to K^{0}\pi^{\pm}\nu$ decay is calculated in a model independent approach where a discrimination of photons in the Bremmstrahlung process is assumed. This correction is completely free of UV and IR singularities and moreover, it satisfies electromagnetic gauge invariance. The result of this work can be applied on the tau decays: $\tau^{\pm}\to \pi^{\pm}\pi^{0}\nu, K^{\pm}\pi^{0}\nu$

PAMELA's cosmic positron from decaying LSP in SO(10) SUSY GUT

We propose two viable scenarios explaining the recent observations on cosmic positron excess. In both scenarios, the present relic density in the Universe is assumed to be still supported by thermally produced WIMP or LSP (\chi). One of the scenarios is based on two dark matter (DM) components (\chi,X) scenario, and the other is on SO(10) SUSY GUT. In the two DM components scenario, extremely small amount of non-thermally produced meta-stable DM component [O(10^{-10}) < n_X /n_\chi] explains the cosmic positron excess. In the SO(10) model, extremely small R-parity violation for LSP decay to e^\pm is naturally achieved with a non-zero VEV of the superpartner of one right-handed neutrino (\tilde{\nu}^c) and a global symmetry.Comment: 6 pages, Talks presented in PASCOS, SUSY, and COSMO/CosPA in 201

Stability Analysis of a Bose-Einstein Condensate Trapped in a Generic Potential

We investigate the dynamical behavior of the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A five-dimensional dynamical system is found (due the symmetry of the Gross-Pitaevskii equation interacting with a potential), where the Thomas-Fermi approximation constrains the parameter space of solutions. We show that for values of the power law exponent equal or smaller than 2 the system seems to be stable. However, when the corresponding exponent is bigger than 2, the instability of the system grows when the power law exponent grows, indicating that large values of the aforementioned parameter can be related to a loss in the number of particles from the condensed state. This fact can be used also to show that the stability conditions of the condensate are highly sensitive to the exponent associated with the external potential.Comment: 9 pages, 2 figure