Quark mixing from Delta(6N^2) family symmetry

TL;DR

This paper explores a model of quark mixing based on the Delta(6N^2) family symmetry, predicting the Cabibbo angle and accommodating small deviations in mixing angles and CP phases.

Contribution

It introduces a specific model using Delta(6N^2) symmetry with N multiple of 7, explaining quark mixing angles and CP phases without breaking residual symmetries.

Findings

Predicted Cabibbo angle |V_us|=0.222521 for N multiple of 7

Model achieves agreement with experimental quark mixing data

Small symmetry-breaking effects (~3%) are compatible with observations

Abstract

We consider a direct approach to quark mixing based on the discrete family symmetry Delta (6N^2) in which the Cabibbo angle is determined by a residual Z_2 times Z_2 subgroup to be $|V_{us}|=0.222521$, for $N$ being a multiple of 7. We propose a particular model in which unequal smaller quark mixing angles and CP phases may occur without breaking the residual Z_2 times Z_2 symmetry. We perform a numerical analysis of the model for $N=14$, where small Z_2 times Z_2 breaking effects of order 3% are allowed by model, allowing perfect agreement within the uncertainties of the experimentally determined best fit quark mixing values.