Dirac Mass Matrices in Gauge Field Theory of Horizontal Symmetry

TL;DR

This paper explores Dirac mass matrices within a gauge field theory of horizontal symmetry, analyzing fermion masses and mixing, and revealing empirical relations and unique mass eigenvalue orderings.

Contribution

It introduces a gauge field theory framework for Dirac mass matrices with a central extension of the Pauli algebra, providing numerical analysis and empirical relations among Yukawa couplings.

Findings

Different orderings in squared mass eigenvalues for up and down quarks.

Empirical relations among Yukawa coupling constants.

Numerical determination of free parameters in mass matrices.

Abstract

We investigate Dirac mass matrices derived in the gauge field theory of a horizontal symmetry generated by a central extension of the Pauli algebra. Through numerical analyses of the observed data of the charged fermion masses and the flavor mixing matrix of quarks, values of free parameters in the mass matrices are determined and several empirical relations are found among the Yukawa coupling constants. As one specific feature of the theory, we find different orderings in squared mass eigenvalues for the up and down quark sectors.