On the hierarchy of neutrino masses

We present a model of neutrino masses combining the seesaw mechanism and strong Dirac mass hierarchy and at the same time exhibiting a significantly reduced hierarchy at the level of active neutrino masses. The heavy Majorana masses are assumed to be degenerate. The suppression of the hierarchy is due to a symmetric and unitary operator R whose role is discussed. The model gives realistic mixing and mass spectrum. The mixing of atmospheric neutrinos is attributed to the charged lepton sector whereas the mixing of solar neutrinos is due to the neutrino sector. Small U_e3 is a consequence of the model. The masses of the active neutrinos are given by $\mu_3\approx\sqrt{\Delta m_{@}^2}$ and $\mu_1/\mu_2\approx \tan^2\theta_\odot$.Comment: 12 pages; Talk presented by M. Jezabek at 'Supersymmetry and Brane Worlds,' Fifth European Meeting Planck 02, Kazimierz, Poland, May 25-29, 2002, to appear in Acta Phys. Polon.

Thomas-Fermi approximation to static vortex states in superfluid trapped atomic gases

We revise the Thomas-Fermi approximation for describing vortex states in Bose condensates of magnetically trapped atoms. Our approach is based on considering the hbar -> 0 limit rather than the N -> infinity limit as Thomas-Fermi approximation in close analogy with the Fermi systems. Even for relatively small numbers of trapped particles we find good agreement between Gross-Pitaevskii and Thomas-Fermi calculations for the different contributions to the total energy of the atoms in the condensate. We also discuss the application of our approach to the description of vortex states in superfluid fermionic systems in the Ginzburg-Landau regime.Comment: 11 pages, 6 figures, revtex4, substantially revised versio

Full sky harmonic analysis hints at large UHECR deflections

The full-sky multipole coefficients of the ultra-high energy cosmic ray (UHECR) flux have been measured for the first time by the Pierre Auger and Telescope Array collaborations using a joint data set with E > 10 EeV. We calculate these harmonic coefficients in the model where UHECR are protons and sources trace the local matter distribution, and compare our results with observations. We find that the expected power for low multipoles (dipole and quadrupole, in particular) is sytematically higher than in the data: the observed flux is too isotropic. We then investigate to which degree our predictions are influenced by UHECR deflections in the regular Galactic magnetic field (GMF). It turns out that the UHECR power spectrum coefficients $C_\ell$ are quite insensitive to the effects of the GMF, so it is unlikely that the discordance can be reconciled by tuning the GMF model. On the contrary, a sizeable fraction of uniformly distributed flux (representing for instance an admixture of heavy nuclei with considerably larger deflections) can bring simulations and observations to an accord.Comment: 8 pages, 4 figures and one table, JETPL style -- v2 as published in JETP