CKM and PMNS mixing matrixes from SO(2) flavor symmetry

Abstract

The relation between quark masses and CKM mixing is studied based on an approximate chiral flavor symmetry of quark mass matrix. In mass hierarchy limit, the mass ratio effect on CKM mixing is suppressed, which separates mass hierarchy and quark flavor mixing into two independent problems. We show that CKM mixing is dominated by two left-handed symmetries while mass hierarchy only provides slight corrections. The same mixing structure is generalized to lepton sector with extended Dirac neutrinos. The common flavor mixing provides a novel comprehension on the relation between quark CKM mixing and lepton PMNS mixing.