A parametrization of the CKM mixing matrix from a scheme of S3L x S3R symmetry breaking

TL;DR

This paper proposes a new parametrization of the CKM matrix based on S3L x S3R symmetry breaking, linking quark mass ratios and CP violation to the structure of the symmetry breaking scheme.

Contribution

It introduces a parametrization of the CKM matrix derived from a specific symmetry breaking scheme, fitting experimental data with a minimal set of parameters.

Findings

The parametrization accurately reproduces CKM matrix element magnitudes.

Constraints on the CP violating phase are derived from the symmetry scheme.

The preferred symmetry breaking scheme is identified based on fit quality.

Abstract

Recent interest in flavour or horizontal symmetry building (mass textures) has been spurred mainly by the large top mass and, hence, the strong hierarchy in quark masses. Recently, various symmetry breaking schemes have been proposed based on the discrete, non-Abelian group S3L x S3R, which is broken according to S3L x S3R > S3_diag > S2_diag. The group S3 treats three objects symmetrically, while the hierarchical nature of the Yukawa matrices is a consequence of the representation structure, 1 + 2, of S3, which treats the generations differently. Different ansaetze for the breaking of the sub-nuclear democracy give different Hermitian mass matrices, M, of the same modified Fritzsch type which differ in the numerical value of the ratio M_23/M_22. A fit to the experimentally determined absolute values of the elements of the CKM matrix gives bounds on the possible values of the CP violating phase and gives a clear indication on the preferred symmetry breaking scheme. A parametrization of the CKM mixing matrix in terms of four quark mass ratios and one CP violating phase in very good agreement with the absolute value of the experimentally determined values of the CKM matrix elements is obtained.