Natural flavor conservation in Higgs induced neutral currents and the quark mixing angles

We present the complete characterization of horizontal symmetries ensuring natural flavor conservation in Higgs induced neutral currents in sequential SU(2)xU(1) models with n generations. The derivation necessitates developing some new mathematics of monomial representation and bi-diagonalization. The conclusion is that there exists a completely chracterized set of horizontal symmetries, which would allow for SU(2) U(1) models with natural flavor conservation. This result extends the well-known condition for natural flavor conservation in the case of a single Higgs, already given by Glashow and Weinberg. For the set of symmetries thus found we show that the corresponding quark mixing matrices (in the tree approximation) all have common features. In particular, the Cabibbo angle, whenever determined, in the tree approximation, by a horizontal symmetry ensuring natural flavor conservation, would be far off its experimental value (the trivial determination being furthermore unaffected by the radiative corrections). (orig.)