Flavour mixing in terms of mass matrices of radiative nature

Abstract

Examines conventional weak isodoublet families (quarks and leptons) within the context of a symmetric ansatz of geometrical scaling for their mass matrix elements. This novel ansatz is due to a radiative mechanism of mass generation and is characterized by the positivity of both the mass matrix elements and the eigenvalues. In the quark sector, the author tests the ability to reproduce the unexpectedly high-lying Vub/Vcb data. The author starts with a two-parameter approximation to the quark mass matrices. It gives ratios of adjacent eigenvalues that are generation independent, and a mixing matrix that exhibits the symmetry Vus approximately=-Vcd approximately=Vcb approximately=-Vts approximately=etc. It is shown that the observed strong violation of this symmetry as well as the observed values of the mixing angles themselves can precisely be reproduced by taking into account the deviation of mb/ms from ms/md. No interesting mass bounds for the fourth-family quark flavours result. The reason is the discovered approximate invariance of the 3*3 parts of the mass matrices and the mixing matrix under the addition of a fourth family. The large top mass predicted by standard model analyses fits naturally into the scheme. In the leptonic sector, the analysis is confined to Dirac neutrinos. General results obtained for the quarks provide a reliable approximation of the neutrino mass matrix.