We review the arguments of anomaly cancellation in the standard model and point out that charge quantization is implied without reference to grand unification. In the absence of any reference to Higgs particles, anomaly cancellation, including the mixed gravitational anomaly, among the standard-model fermions yields two possible hypercharge assignments, one of which is the standard one. The uniqueness of the hypercharge assignments is recovered by extending the standard-model fermions by a right-handed neutrino and enlarging the gauge group to ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\times {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$.

• Received 12 July 1989

DOI:https://doi.org/10.1103/PhysRevD.41.715