Generalization of the Pati-Salam model

The Pati-Salam model for unified lepton-hadron symmetry is extended to incorporate $\mathrm{SU}{\mathrm{}\left(2l\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2l\right)\mathrm{}}_R\times \mathrm{SU}\mathrm{}\left(4\right)\mathrm{}$ gauge symmetry in order to include models containing 4, 6, or more fractionally charged quarks. A symmetry-breaking scheme for the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{SU}\mathrm{}\left(4\right)\mathrm{}$ subgroup containing all known interactions is developed for arbitrary values of $l$. The symmetry-breaking procedure leads to the Weinberg theory of weak interactions in a natural way. The Weinberg angle is expressed in terms of the coupling constants and dimensionality $l$ of the theory. Implications of embedding the $\mathrm{SU}{\mathrm{}\left(2l\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2l\right)\mathrm{}}_R\times \mathrm{SU}\mathrm{}\left(4\right)\mathrm{}$ group in a universal gauge group are discussed. In such a model ${{sin}^2\theta }_W=\frac{3}{8}$ independent of $l$.