Saturation of Quark Forces in Zero-Triality States

We consider the Han-Nambu quark model, in which the internal symmetry group of hadrons is $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$, and we attempt to find a mechanism such that the masses of $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$ singlets are much lower than those of other $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$ multiplets. One possibility is to assume the existence of a massive vector "supermeson" strongly coupled to the (1,8′) part of the quark current. The lowest energy state of the supermeson field would favor $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$ singlets, just as the lowest energy state of the electromagnetic field is reached when all matter is neutral. These supermesons, if sufficiently massive, would be rather difficult to observe. Another possibility (which effectively corresponds to the limit of supermesons with infinite mass) is to assume a four-quark interaction of the current-current type. With a suitable form of this interaction, $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$ singlets again have masses much lower than those of other $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^{\prime }$ multiplets.