Quarks Mixing in Chiral Symmetries

Abstract

We discuss a subject of the quarks mixing in SU4∗SU4 and SU6∗SU6 symmetries trying to calculate the quarks mixing angles and the complex phase responsible for the CP non-conservation on the basis of the Gell-Mann Oakes Renner model. Assuming symmetry breaking in a limit of exact sub-symmetries for simultaneous quarks rotations in both electric charge sub-spaces we can estimate all mention above parameters. A perfect agreement of the experimental value of the Cabibbo angles with a sum of simultaneous quarks mixing angles in doublets (u,c) and (d,s) in the SU4∗SU4 symmetry suggests that a quarks mixing is realized in a maximal allowed range. The same assumption used for the SU6∗SU6 and a simultaneous maximal allowed quarks mixing in both electric charge triplets (u,c,t) and (d,s,b) gives a perfect agreement with the experimental value of the Cabibbo angle and estimation on the angles Θ2 and Θ3 as well as a bond for the complex phase δ.