Constraints on gauge theories with diagonal neutral currents

Abstract

We derive constraints for the representation content of SU(2) × U(1) gauge theories, whose neutral weak interactions conserve all flavors. Among the results are the following: (a) For theories where all right-handed quarks are singlets under weak isospin, the existence of quarks with different values of ${T_L}^2$ and $Y_L$ implies one or more conservation laws in addition to charge. (b) In models with quarks of charges $\frac{2}{3}$ and $-\frac{1}{3}$ and no new conservation laws we find that there are only three possibilities: (i) a generalization of the standard model with left-handed doublets and right-handed singlets, (ii) its mirror image, and (iii) a pure vector model with all quarks in doublets on the right and on the left, with degenerate masses for quarks of the same charge.