Spectrum of the excited ${N}^{*}$ and ${\mathrm{\ensuremath{\Delta}}}^{*}$ baryons in a relativistic chiral quark model

Spectrum of the excited $N^{}$ and $Δ^{}$ baryons in a relativistic chiral quark model

E. M. Tursunov and S. Krewald

Phys. Rev. D 90, 074015 – Published 10 October 2014

Abstract

The spectrum of the SU(2) flavor baryons is studied in the frame of a relativistic chiral quark potential model based on the one-pion and one-gluon exchange mechanisms. It is argued that the $N^{*}$ and $Δ^{*}$ resonances strongly coupled to the $π N$ channel are identified with the orbital configurations $(1 S_{1 / 2})^{2} (n l j)$ with a single valence quark in the excited state ( $n l j$ ). With the obtained selection rules based on the “chiral constraint,” we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data and yielding no “missing resonances.” A new original method for the treatment of the center of mass problem is suggested which is based on the separation of the three-quark Dirac Hamiltonian into the parts, corresponding to the Jacobi coordinates. The numerical estimations for the energy positions of the nucleon and delta baryons (up to and including F-wave $N^{*}$ and $Δ^{*}$ resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data at the level of the relativized constituent quark model of S. Capstick and W. Roberts without any fitting parameters. The only free parameter of the linear confinement potential was fitted previously by Th. Gutsche to reproduce the axial charge of the nucleon. The ground state $Δ (1232)$ is well reproduced. However, nucleon ground state and most of the radially excited baryon resonances (including Roper) are overestimated. On the contrary, the first band of the orbitally excited baryon resonances with a negative parity are underestimated. At the same time, the second band of the orbitally excited $Δ^{*}$ states with the negative parity are mostly overestimated, while the $N^{*}$ states are close to the experimental boxes. The theoretical estimations of the energy levels for the positive parity baryon resonances with $J = 5 / 2$ , $7 / 2$ are close to the experimental data. At higher energies, where the experimental data are poor, we can extend our model schematically and predict an existence of seven $N^{*}$ and four $Δ^{*}$ new states with larger spin values.