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

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.