Lepton mixing from the hidden sector

Experimental results indicate a possible relation between the lepton and quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X is a matrix with special structure related to the mechanism of neutrino mass generation. We propose a framework which can realize such a relation. The main ingredients of the framework are the double seesaw mechanism, SO(10) Grand Unification and a hidden sector of theory. The latter is composed of singlets (fermions and bosons) of the GUT symmetry with masses between the GUT and Planck scale. The interactions in this sector obey certain symmetries G_hidden. We explore the conditions under which symmetries G_hidden can produce flavour structures in the visible sector. Here the key elements are the basis-fixing symmetry and mediators which communicate information about properties of the hidden sector to the visible one. The interplay of SO(10) symmetry, basis-fixing symmetry identified as Z2 x Z2 and G_hidden can lead to the required form of U_X. A different kind of new physics is responsible for generation of the CKM mixing. We present the simplest realizations of the framework which differ by nature of the mediators and by symmetries of the hidden sector.Comment: 30 pages, 6 figures; typo corrected, one reference added, version for publication in Phys. Rev.

Atmospheric neutrinos: LMA oscillations, Ue3 induced interference and CP-violation

We consider oscillations of the low energy (sub-GeV sample) atmospheric neutrinos in the three neutrino context. We present the semi-analytic study of the neutrino evolution and calculate characteristics of the e-like events (total number, energy spectra and zenith angle distributions) in the presence of oscillations. At low energies there are three different contributions to the number of events: the LMA contribution (from electron-neutrino oscillations driven by the solar oscillation parameters), the Ue3-contribution proportional to s13**2, and the Ue3 - induced interference of the two amplitudes driven by the solar oscillation parameters. The interference term is sensitive to the CP-violation phase. We describe in details properties of these contributions. We find that the LMA, the interference and Ue3 contributions can reach 5 - 6%, 2 - 3% and 1 - 2 % correspondingly. An existence of the significant (> 3 - 5 %) excess of the e-like events in the sub-GeV sample and the absence of the excess in the multi-GeV range testifies for deviation of the 2-3 mixing from maximum. We consider a possibility to measure the deviation as well as the CP- violation phase in future atmospheric neutrino studies.Comment: 30 pages, RevTeX4.0, 11 figures; improved figure

Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.Comment: 6 pages, late

Structure of Matrix Elements in Quantum Toda Chain

We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these integrals are discussed. We explain that these properties are necessary in order to provide the correct number of independent operators. The comparison with the classical theory is done.Comment: LaTeX, 17 page

IBM: parameter symmetry, hidden symmetries and transformations of boson operators

A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed.Comment: LATEX, 11 pages including 1 eps figure and 1 table prepared as an eps figure; a talk given by A. M. Siirokov at XXII Symposium on Nuclear Physics, Oaxtepec, Morelos, M\'exico, 5--8 January, 1999; to be published in Revista Mex. Fi