Rare semileptonic meson decays in R-parity violating MSSM

We discuss rare meson decays $K^ + \to \pi ^ - \ell ^ + \ell '^ +$ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell, \ell'=e, \mu$) in a supersymmetric extension of the Standard Model with R-parity violation. Estimates of the branching ratios for these decays are presented.Comment: 5 pages, 1 figure; title modified to better reflect the contents, a normalization error corrected for D-meson decays, modifying parts of Table 1; a reference and DESY Report number added; to appear in the Proceedings of the 12th. Lomonosov Conference on Elementary Particle Physics, Moscow State University, Moscow, Russia, 25-31 August 200

Bilinear R-parity Violation in Rare Meson Decays

We discuss rare meson decays $K^ + \to \pi ^ - \ell ^ + \ell '^ +$ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell ,\ell ' = e,\mu$) in a supersymmetric extension of the standard model with explicit breaking of R-parity by bilinear Yukawa couplings in the superpotential. Estimates of the branching ratios for these decays are given. We also compare our numerical results with analogous ones previously obtained for two other mechanisms of lepton number violation: exchange by massive Majorana neutrinos and trilinear R-parity violation.Comment: 5 pages, 1 figure; To appear in the Proceedings of the 13th Lomonosov Conference on Elementary Particle Physics, 23 -- 29 August, 2007, Moscow, Russi

Lepton pair production by high-energy neutrino in an external electromagnetic field

The process of the lepton pair production by a neutrino propagating in an external electromagnetic field is investigated in the framework of the Standard Model. Relatively simple exact expression for the probability as the single integral is obtained, which is suitable for a quantitative analysis.Comment: 9 pages, LATEX, 2 PS figures, submitted to Modern Physics Letters

Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum