We discuss the problem of defining a residual global symmetry for classification purposes in the context of a spontaneously broken gauge theory of strong, weak, and electromagnetic interactions, where strong interactions are associated with a local color SU(3)′ group. We show that a weakly broken $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_c$ [different from but related to SU(3)′] can always be realized as a good classification symmetry for a class of models with integer-charge quarks and massive gluons. For fractionally charged quark models, the symmetry $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_c$ is exact even for massive gluons, only if the full theory contains an Abelian U(1) symmetry associated with electric charge. If there is no such U(1) symmetry in the theory, and we wish to preserve a three-color classification symmetry in the fractionally charged quark model, then the gluons must be left massless.

• Received 10 July 1975

DOI:https://doi.org/10.1103/PhysRevD.13.1733