The smallness of fermion masses and mixing angles has recently been attributed to approximate global U(1) symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor-changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much $\mathrm{CP}$ violation in the neutral kaon mass matrix. Hence in these theories $\mathrm{CP}$ must also be a good approximate symmetry. Such models provide an alternative mechanism for $\mathrm{CP}$ violation and have various interesting phenomenological features.

• Received 4 May 1993

DOI:https://doi.org/10.1103/PhysRevD.48.R979