Leptophobic U(1)'s and theRb−Rcanomalies

In this paper, we investigate the possibility of explaining both the $R_b$ excess and the $R_c$ deficit reported by the CERN LEP experiments through $Z-Z^{\prime }$ mixing effects. We have constructed a set of models consistent with a restrictive set of principles: unification of the standard model (SM) gauge couplings, vector-like additional matter, and couplings which are both generation independent and leptophobic. These models are anomaly-free, perturbative up to the GUT scale, and contain realistic mass spectra. Out of this class of models, we find three explicit realizations which fit the LEP data to a far better extent than the unmodified SM or MSSM and satisfy all other phenomenological constraints which we have investigated. One realization, the $\eta$ model coming from ${\mathrm{E}}_6$, is particularly attractive, arising naturally from geometrical compactifications of heterotic string theory. This conclusion depends crucially on the inclusion of a U(1) kinetic mixing term, whose value is correctly predicted by renormalization group running in the ${\mathrm{E}}_6$ model given one discrete choice of spectra.