Unitarity polygons and CP violation areas and phases in the standard electroweak model

Abstract

A geometrical interpretation of CP violation in terms of areas of unitarity triangles is presented, in the standard electroweak model with three families of quarks. The extension of the results to the case of four families is investigated. A special case is worked out in detail where it is shown how one determines the CP violating invariant phases and the areas of the CP violation triangles as functions of the moduli of the elements of the quark mixing matrix. For the most general four-family case, which is found to be rather involved, the necessary formulae, for determining the invariant phases and the CP violation areas, are given.