Searching for the quark--diquark systematics of baryons composed by light quarks $q=u,d$

Supposing quark--diquark structure of baryons, we look for systematics of baryons composed of light quarks ($q=u,d$). We systematize baryons using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We consider several schemes for the composed baryons: (1) with different diquark masses, $M_{D^0_0} \ne M_{D^1_1}$, (2) with $M_{D^0_0} = M_{D^1_1}$ and overlapping $qD^0_0$ and $qD^1_1$ states (resonances), (3) with/without SU(6) constraints for low-lying states (with quark--diquark orbital momenta L=0). In the high-mass region the model predicts several baryon resonances at $M\sim 2.0-2.9$ GeV. Moreover, the model gives us the double pole structure (i.e. two poles with the same Re$M$ but different Im$M$) in many amplitudes at masses $M\ga 2.0$ GeV. We see also that for description of low-lying baryons (with L=0), the SU(6) constraint is needed.