The Cabibbo angle in a supersymmetric [formula omitted] model

Abstract

We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element | V u d | can take the value | V u d | = cos ( π 14 ) ≈ 0.97493 implying that the Cabibbo angle θ C is sin ( θ C ) ≈ | V u s | ≈ sin ( π 14 ) ≈ 0.2225 . These values are very close to those observed in experiments. The value of | V u d | ( θ C ) is based on the fact that different Z 2 subgroups of D 14 are conserved in the up and down quark sector. In order to achieve this, D 14 is accompanied by a Z 3 symmetry. The spontaneous breaking of D 14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D 14 and partly due to a Froggatt–Nielsen symmetry U ( 1 ) FN under which only the right-handed quarks transform. The model is natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for | V u d | . Out of these, only one of them leads to a phenomenological viable model. A study of the Z 2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow | V u d | ( θ C ) to be well inside the small experimental error bars.