Multiquark baryons and the MIT bag model

The calculation of masses of $q^4\overline{q}$ and $q^5{\overline{q}}^2$ baryons is carried out within the framework of Jaffe's approximation to the MIT bag model. A general method for calculating the necessary SU(6) ⊃ SU(3) ⊗ SU(2) coupling coefficients is outlined and tables of the coefficients necessary for $q^4\overline{q}$ and $q^5{\overline{q}}^2$ calculations are given. An expression giving the decay amplitude of an arbitrary multiquark state to arbitrary two-body final states is given in terms of SU(3) Racah and $9-\lambda \mu$ recoupling coefficients. The decay probabilities for low-lying $\frac{1}{2^{-}}$ $q^4\overline{q}$ baryons are given and compared with experiment. All low-lying $\frac{1}{2^{-}}$ baryons are found to belong to the same SU(6) representation and all known $\frac{1}{2^{-}}$ resonances below 1900 MeV may be accounted for without the necessity of introducing $P$-wave states. The masses of many exotic states are predicted including a $\frac{1}{2^{-}}$ $Z_0^{*}$ at 1650 MeV and $\frac{1}{2^{-}}$ hypercharge -2 and +3 states at 2.25 and 2.80 GeV, respectively. The agreement with experiment for the $\frac{3}{2^{-}}$ and $\frac{5}{2^{-}}$ baryons is less good. The lowest $q^5{\overline{q}}^2$ state is predicted to be a $\frac{1}{2^{+}}$ ${\Lambda }^{*}$ at 1900 MeV.