Flavor-changing scalar interactions.

The smallness of fermion masses and mixing angles has recently been 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 CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features. ∗Research supported in part by NSF grant PHY90-21139 and DOE contract DE-AC0376SF 00098. ∗∗Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY 9009850. The inclusion of multiple scalar doublets at the weak scale in the standard SU(2) ⊗ U(1) electroweak theory entails the risk of flavor-changing neutral current processes with rates in excess of experimental bounds. To avoid this, most studies of such models have adopted the proposal of a global symmetry that allows only one scalar doublet to couple to the right-handed quarks of each charge. Recently the need for such a symmetry has been challenged in an article that attributes the various small ratios among quark mixing angles and quark and lepton masses to a set of approximate global U(1) symmetries that act only on the quarks, but not on the scalars. Specifically, it is assumed that every appearance of a fermion of the i’th generation in a Yukawa interaction of quarks or leptons with any scalar doublet φn is accompanied with a small dimensionless factor: ǫQi for left-handed quark doublets; ǫUi or ǫDi for right handed quarks; ǫLi for left-handed lepton doublets; and ǫEi for right-handed charged leptons. That is, writing the general Yukawa interaction in the form LY = −λijnQ̄LiURj · φ̃n − λijnQ̄LiDRj · φn − λijnL̄LiERj · φn +H.c., (1) QLj ≡ [