Minimal anomaly-free electroweak model for several generations

A horizontal U′(1) gauge symmetry is invoked to distinguish several fermion generations which have the one and the same Weinberg-Salam (WS) structure. It is assumed that both weak hypercharges associated with the WS U(1) and the new U′(1) factorize, i. e., they are of the form λiy and λ′iy′, where the scales λi,λ′i are the so-called seriality numbers of the ith generation. The motivation for such an assumption comes from the standard WS model, where the anomaly constraints determine the Y quantum numbers for a given generation up to a common scale. The generation structure is extended to the Higgs system as well, i.e., associated with the ith generation, there is an ith Higgs doublet whose U′(1) hypercharge is λ′ih where h is a number. We study as a prototype the simplest but the fundamental two-generation scheme in detail and show how when the above assumptions are combined with (a) anomaly-free conditions, (b) conservation of lepton numbers, and (c) the emergence of a proper Cabibbo structure, we are led to a unique choice for Y′ which can be expressed as Y′=[Y3+2(B-L)3] with the signs being the seriality numbers for the two generations, respectively. A hierarchy in the vacuum expectation values (VEV's) of the Higgs doublets produces the desired hierarchy in the fermion masses, and correlates the smallness of me with the smallness of mu, md, and θC. The gauge boson associated with U′(1) produces of course the undesirable flavor-changing neutral currents and the violation of e-μ universality. However, an additional Higgs singlet with zero Y and with a large VEV suffices to make the mass of Z′ heavy enough to suppress the unwanted features to any desirable degree. From the KL-KS mass difference we estimate M(Z′)>(1α)M(Z). We investigate briefly a three-generation scheme within the framework of the present model and argue that it fits more naturally in an [SU(2)×U(1)]WS×U′(1)N model for 2N generations. Thus, from our point of view, the existence of a third generation suggests the existence of a fourth one as well.