Quark mass matrices and generation mixing in the standard model with non-commutative geometry

Abstract

A version of the standard model using non-commutative geometry allows to classify three quark generations in a twelve-dimensional, reducible, but indecomposable representation which provides a natural framework for inter-generational interactions. Assuming the quark generations to be initially degenerate (thus blaming electroweak interactions for the observed splittings) we find mass matrices and CKM mixing identical with, or very close to, published empirical analyses in agreement with experiment but derived from a very different physical picture. We present fully analytic expressions for the mass matrices and the mixing matrices which are functions of the mass eigenvalues and a small number of parameters. Our results confirm our previous experience: models based on non-commutative geometry explain some of the qualitative features of the standard model which previously were empirical inputs.