Hierarchical majorana neutrinos from democratic mass matrices

In this paper, we obtain the light neutrino masses and mixings consistent with the experiments, in the democratic texture approach. The essential ansatz is that $\nu_{Ri}$ are assumed to transform as "right-handed fields" $\bf 2_{R} + 1_{R}$ under the $S_{3L} \times S_{3R}$ symmetry. The symmetry breaking terms are assumed to be diagonal and hierarchical. This setup only allows the normal hierarchy of the neutrino mass, and excludes both of inverted hierarchical and degenerated neutrinos. Although the neutrino sector has nine free parameters, several predictions are obtained at the leading order. When we neglect the smallest parameters $\zeta_{\nu}$ and $\zeta_{R}$, all components of the mixing matrix $U_{\rm PMNS}$ are expressed by the masses of light neutrinos and charged leptons. From the consistency between predicted and observed $U_{\rm PMNS}$, we obtain the lightest neutrino masses $m_{1}$ = (1.1 $\to$ 1.4) meV, and the effective mass for the double beta decay \vev{m_{ee}} \simeq 4.5 meV.Comment: 14 pages, 1 table, substantially revised versio

Flavor structure from misalignment of inner products in noncommutative geometry

In this letter, we consider an idea that induces flavor structure from inner products in noncommutative geometry. Assuming proper components of vectors $v_{(L,R) i}$ in enlarged representation space for fermions, we can induce the waterfall texture for Yukawa matrices retaining gauge interactions are universal. The hierarchy of the Yukawa interactions is a consequence of "misalignment" between the vectors $v_{Li}$ and $v_{Rj}$.Comment: 6pages, 1 table, the final version to appear in JHE

Effect of lift force on the aerodynamics of dust grains in the protoplanetary disk

We newly introduce lift force into the aerodynamics of dust grains in the protoplanetary disk. Although many authors have so far investigated the effects of the drag force, gravitational force and electric force on the dust grains, the lift force has never been considered as a force exerted on the dust grains in the gas disk. If the grains are spinning and moving in the fluid, then the lift force is exerted on them. We show in this paper that the dust grains can be continuously spinning due to the frequent collisions so that the lift force continues to be exerted on them, which is valid in a certain parameter space where the grain size is larger than ~ 1 m and where the distance from the central star is larger than 1 AU for the minimum mass solar nebula. In addition, we estimate the effects of the force on the grain motion and obtain the result that the mean relative velocity between the grains due to the lift force is comparable to the gas velocity in the Kepler rotational frame when the Stokes number and lift-drag ratio are both ~ 1. This estimation is performed under the assumptions of the steady state and the isotropic spin angular momentum. We also estimate the mean relative velocity when the grains keep spinning and conclude that the lift force marginally affects the mean relative velocity in the minimum mass solar nebula. If there is a grain-concentrated part in the disk, the relative velocity due to the lift force may dominate there because of high collision rate.Comment: 9 pages, 4 figures. Accepted for publication in Earth, Planets and Spac