Quark--Diquark Systematics of Baryons and the SU(6)SYMMETRY for Light States

We continue our attempts to systematize baryons, which are composed of light quarks ($q=u,d$), as quark–diquark systems. The notion of two diquarks is used: (i) $D_1^1$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) $D_0^0$, with $S_D=0$ and $I_D=0$. Here we try to resolve the problem of the low-lying $\mathrm{\Delta }({\frac{5}{2}}^{-})$ states: in the last experiments the lightest state is observed at $\text{ga}2200$ MeV, not at $1900-2000$ MeV as it has been stated 20 years ago. We are looking for different systematization variants with the forbidden low-lying $\mathrm{\Delta }({\frac{5}{2}}^{-})$ states in the mass region $\la 2000$MeV\mathrm{.}WeseethattheinclusionoftheSU(6)constraintson$qD^{1}_{1}$stateswithangularmomentumL=1resultsinashiftofthelightest$\Delta(\frac 52^-)$isobarto$\sim 2300$ MeV. The scheme with the SU(6) constraints for low-lying $q{D}_1^1$ and $q{D}_0^0$ states (with $L=0,1$) is presented in detail here.