BrokenSU(4)⊗SU(4)symmetry

Starting with chiral $\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(4\right)\mathrm{}$ invariance realized in the Nambu-Goldstone manner, with the vacuum invariant under SU(3), we discuss in this paper the various implications of explicit symmetry-breaking terms that transform as the $(4,4^{*})\oplus (4^{*},4)$ representation. The motivation for this work comes from recent investigations in connection with the unified gauge theories, which suggest the relevance of $\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(4\right)\mathrm{}$ symmetry of strong interactions with $(4,4^{*})\oplus (4^{*},4)$ breaking. The domain structure for the allowed values of the symmetry-breaking parameters is discussed in analogy with a similar investigation for the $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$ theory, and the ratio of charmed- to uncharmed-particle masses is derived in terms of these parameters. Solutions are sought for these parameters through an analysis of the $\eta -\chi$ and $\eta -\chi -E$ mixing problems, as well as $\eta$, $\chi \to 2\gamma$ decays. Within the framework of our assumptions, we are unable to obtain a solution that agrees with the recent results discussed by Dittner et al. on the basis of a hadronlepton analogy.