$SU(3)_c\otimes SU(4)_{\mathrm {L}}\otimes U(1)_X$ model for three families

Abstract

An extension of the standard model to the local gauge group $SU(3)_c\otimes SU(4)_{\mathrm {L}}\otimes U(1)_X$ as a three-family model is presented. The model does not contain exotic electric charges and we obtain a consistent mass spectrum by introducing an anomaly-free discrete Z 2 symmetry. The neutral currents coupled to all neutral vector bosons in the model are studied. By using experimental results from the CERN LEP, SLAC Linear Collider and atomic parity violation data we constrain the mixing angle between two of the neutral currents in the model and the mass of the additional neutral gauge bosons to be $-0.0032\leq\sin\theta\leq 0.0031$ and $0.67 \hbox{TeV}\leq M_{Z_2} \leq 6.1$ TeV at $95 \%$ C.L., respectively.