The CKM matrix with maximal CP violation from Z(12) symmetry

TL;DR

This paper proposes a model using Z(12) discrete symmetry to explain the maximal CP violation phase in the CKM matrix, aligning with recent precise measurements of quark mixing parameters.

Contribution

It introduces a supersymmetric Z(12) symmetry model that accounts for the maximal CP phase in the CKM matrix, linking discrete symmetry to quark mass textures.

Findings

Maximal CP phase of 90 degrees explained by Z(12) symmetry.

Quark mass matrix elements follow a lambda^6 power pattern.

Model aligns with recent accurate CKM parameter measurements.

Abstract

The recent accurate determination of the CKM parameters including the maximal CP phase 90 degrees enables us to write down the up-type and down-type quark mass matrices to a high degree of accuracy. The lightest element(the uu element) of the quark mass texture (not the mass eigenvalue) has a power lambda**6 where lambda=sin(Cabibbo angle). The CP phase of 360 degrees divided by an integer hints a discrete symmetry. Since lambda**6 is the highest power among the quark mass matrix elements, we present as an example a possibility that the maximal CP phase 90 degrees is obtainable from a supersymmetric Z(12) discrete symmetry model.