The notion that there exists a fundamental quark-lepton symmetry is proposed. To implement this symmetry, leptons (as well as quarks) are assumed to come in three "colors," i.e., the gauge group of the world is assumed to be ${\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}}_q\otimes {\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}}_l\otimes {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\otimes {\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_y$. From the consistency considerations of gauge invariance and anomaly cancellation we "derive" the form of a $Z_2$ discrete symmetry which transforms quarks to leptons (and leptons to quarks). We show that such a theory can reproduce the standard model at low energies (i.e., $\sqrt{s}\le 100$ GeV), and hence quark-lepton symmetry may be realized in nature.

• Received 12 October 1989

DOI:https://doi.org/10.1103/PhysRevD.41.3502