Gauge model for the strong interactions

A gauge theory is introduced with the gauge group $\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{y^{\prime }}$. In this theory the quarks transform under the fundamental four-dimensional representation of SU(4). Gauge anomaly cancellation is imposed on the known fermion generation structure (with four colors) to fix the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{y^{\prime }}$ charges. It is shown that the model requires the existence of only one extra Higgs multiplet to break the SU(4) group to $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_c$ and at the same time give the exotic $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_c$-singlet quarks mass. The model has the novel feature that the unbroken electric charge generator is embedded in all three simple factor groups of the semisimple gauge group.