The conflict between natural flavor conservation of Higgs couplings and cabibbo mixing in SU(2)L × U(1)

The general problem of conservation of strangeness and other quark flavors by the exchange of several neutral Higgs mesons is investigated in SU(2)_L × U(1). We find that the horizontal symmetries necessary to enforce this conservation conflict with the known Cabibbo mixing. In particular, if the quarks form an irreducible representation of the horizontal symmetry, the mixing angles are all trivial (i.e., 0 or $\text{π}\text{2}$); if they form a reducible representation, it is possible to have some nontrivial mixing angles, but only if there are several unmixed generations of quarks with exactly the same relative pattern of masses and mixings.