Generalization of the Glashow-Iliopoulos-Maiani mechanism: Horizontal and vertical flavor mixing

For theories with more than four quarks we generalize the Glashow-Iliopoulos-Maiani mechanism for flavor-change suppression in the gauge sector and the Glashow-Weinberg theorems for the corresponding suppression in the Higgs sector. We note that there is a class of theories in which many but not all flavor changes are naturally suppressed. $d\leftrightarrow s$ and $u\leftrightarrow c$ are in the naturally suppressed category. Such theories have distinctive experimental signatures. We discuss the simplest example where the new mechanism applies: SU(3) × U(1) with six quarks, two with charge $\frac{2}{3}$, four with charge $-\frac{1}{3}$. We also indicate how this six-quark system can be incorporated in a full-fledged gauge theory.