A periodic table for the excited Nucleon and Delta spectrum in a relativistic chiral quark model

Abstract

A possibility of the construction of a periodic table for the excited baryon spectrum is shown in the frame of a relativistic chiral quark model based on selection rules derived from the one-pion exchange mechanism. It is shown that all the $N^*$ and $\Delta^*$ resonances appearing in the $\pi N$ scattering data and strongly coupling to the $\pi N$ channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$. Baryon resonances corresponding to the orbital configuration with two valence quarks in excited states couple strongly to the $\pi \pi N$-channel, but not to the $\pi N$ channel. At low energy scale up to 2000 MeV, the obtained numerical estimations for the SU(2) baryon states (up to and including F-wave $N^*$ and $\Delta^*$ resonances) within the schematic periodic table are mostly consistent with the experimental data. It is argued that due-to the overestimation of the ground state N(939) and Roper resonance N(1440) almost by the same amount and that the Roper resonance is a radial excitation of the N(939), the "lowering mechanism" for the both baryon states must be the same. The same mechanism is expected in the $\Delta$ sector. At higher energies, where the experimental data are poor, we can extend our model schematically and predict seven new $N^*$ and four $\Delta^*$ resonances with larger spin values.