Quark mixings as a test of a new symmetry of quark Yukawa couplings

Based on the hierarchy exhibited by quarks masses at low energies, we assume that Yukawa couplings of up and down quarks are related by $Y_u\propto Y_d^2$ at grand unification scales. This ansatz gives rise to a symmetrical CKM matrix at the grand unification (GU) scale. Using three specific models as illustrative examples for the evolution down to low energies, we obtain the entries and asymmetries of the CKM matrix which are in very good agreement with their measured values. This indicates that the small asymmetry of the CKM matrix at low energies may be the effect of the renormalization group evolution only.Comment: LaTeX file, 10 pages including 1 tabl

Renormalization group evolution of the CKM matrix

We present here the most important ideas, equations and solutions for the running of all the quark Yukawa couplings and all the elements of the Cabibbo-Kobayashi-Maskawa matrix, in the approximation of one loop, and up to order $\lambda ^{4}$, where $\lambda \sim 0.22$ is the sine of the Cabibbo angle. Our purpose is to determine what the evolution of these parameters may indicate for the physics of the standard model (SM), the minimal supersymmetric standard model (MSSM) and for the Double Higgs Model (DHM).Comment: Talk given in the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 2002. 6 pages, LaTeX, needs aipproc.cls styl

Lie antialgebras: cohomology and representations

We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We formulate classification theorems and give a number of examples.Comment: 11 pages, XXVII Workshop, Geometrical Methods in Mathematical Physics., Bialowieza : Pologne (2008

Lorentz Covariant Distributions with the Spectral Conditions

The Lorentz covariant tempered disributions with the supports in the product of the closed upper light cones are described.Comment: 13 page