NATURAL RELATIONS BETWEEN THE CABIBBO ANGLE AND QUARK MASSES IN SU(2)LXU(1) WITH 4 FLAVORS

A complete classification of all possible natural relations between the Cabibbo angle Θc and quark masses is given which follow from an arbitrary horizontal symmetry H (discrete or continuous) and the standard gauge group SU(2)L×U(1) with four quark flavours. It is shown that such relations depend basically only on the dimensions of the fermion and Higgs representations and that they are therefore identical for all H with representations of the same dimensions and with the same Clebsch-Gordan series for the relevant Kronecker products. If Θc depends on quark masses only, then either Θc≃md/ms or {Mathematical expression}. In particular, the phenomenologically successful relation {Mathematical expression} cannot be obtained in a natural way in the 4-flavour SU(2)L×U(1) model for any horizontal symmetry. © 1979 Springer-Verlag.