Geometry of Majorana neutrino and new symmetries

Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of binary Cartan--Killing--Lie symmetries/supersymmetries. As one of the very important applications of such new ternary symmetries could be related with explanation of the nature of the three families and three colour symmetry. The Majorana neutrino can directly indicate the existence of a new extra-dimensional geometry and thanks to new ternary space-time symmetries, could lead at high energies to the unextraordinary phenomenological consequences.Comment: The article is presented on the 2-nd Simposium on Neutrinos and Dark Matter in Nuclear Physics, Paris, September 3-9, 200

The decays ρ−→ηπ−\rho^{-}\to\eta\pi^{-} and τ−→η(η′)π−ν\tau^{-}\to\eta(\eta')\pi^{-}\nu in the NJL model

The widths of the decays $\rho^{-}\to\eta\pi^{-}$ and $\tau^{-}\to\eta(\eta')\pi^{-}\nu$ are calculated in the framework of the NJL model. It is shown that these decays are defined by the $u$ and $d$ quark mass difference. It leads to the suppression of these decays in comparison with the main decay modes. In the process $\rho^{-}\to\eta\pi^{-}$ the intermediate scalar $a_0^{-}$ state is taken into account. For the $\tau$ decays the intermediate states with $a_0^{-}$, $\rho^{-}(770)$ and $\rho^{-}(1450)$ mesons are used. Our estimates are compared with the results obtained in other works.Comment: 6 pages, 5 figures, 1 tabl

Ternary numbers and algebras. Reflexive numbers and Berger graphs

The Calabi-Yau spaces with SU(m) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the $n$-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras, ${\mathbb R}$, ${\mathbb C}$, ${\mathbb H}$, ${\mathbb O}$, which helped to discover the most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case $n=3$, which gives the ternary generalization of quaternions and octonions, $3^p$, $p=2,3$, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra and group which are related to the natural extensions of the binary $su(3)$ algebra and SU(3) group. Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.Comment: Revised version with minor correction

The processes e+e−→ππ(π′)e^{+}e^{-} \to \pi\pi(\pi') in the extended NJL model

The process $e^{+}e^{-} \to \pi^{+}\pi^{-}$ is described in the framework of the extended NJL model. Intermediate vector mesons $\rho^0(770)$, $\omega(782)$ and \rho'(1450)$are taken into account. Our results are in satisfactory agreement with experimental data. The prediction for the process$e^{+}e^{-} \to \pi\pi'(1300)$is given. Here the main contribution is given by the diagram with intermediate$\rho'(1450)$ meson.Comment: 7 pages, 5 figure

Root systems from Toric Calabi-Yau Geometry. Towards new algebraic structures and symmetries in physics?

The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from $CY_3$ reflexive polyhedra. We show how some particularly defined integral matrices can be assigned to these diagrams. This family of matrices and its associated graphs may be obtained by relaxing the restrictions on the individual entries of the generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These graphs keep however the affine structure, as it was in Kac-Moody Dynkin diagrams. We presented a possible root structure for some simple cases. We conjecture that these generalized graphs and associated link matrices may characterize generalizations of these algebras.Comment: 24 pages, 6 figure

THE NUMBER OF SPHALERON INSTABILITIES OF THE BARTNIK-McKINNON SOLITONS AND NON-ABELIAN BLACK HOLES

It is proven that there are precisely $n$ odd-parity sphaleron-like unstable modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.Comment: one reference is adde

Cosmic Colored Black Holes

We present spherically symmetric static solutions (a particle-like solution and a black hole solution) in the Einstein-Yang-Mills system with a cosmological constant.Although their gravitational structures are locally similar to those of the Bartnik-McKinnon particles or the colored black holes, the asymptotic behavior becomes quite different because of the existence of a cosmological horizon. We also discuss their stability by means of a catastrophe theory as well as a linear perturbation analysis and find the number of unstable modes.Comment: 12 pages, latex, 4 figures (available upon request