The spectrum of the excited $N^*$ and $Δ^*$ baryons in a relativistic chiral quark model

Details The spectrum of the excited $N^*$ and $Δ^*$ baryons in a relativistic chiral quark model The spectrum of the excited $N^*$ and $Δ^*$ baryons in a relativistic chiral quark model

2012-04-02

arxiv.org/abs/1204.0412v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages, 2 figures, 2 tables. The text has been edited and improved essentially, new figures added. arXiv admin note: substan

Scientific paper

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 $\Delta^*$ resonances appearing in the $\pi N$ scattering data and strongly coupled to the $\pi N$ channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$ with a single valence quark in the excited state $(nlj)$. Based on obtained selection rules we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data. The numerical estimations for the energy positions of the Nucleon and Delta baryons (up to and including F-wave $N^*$ and $\Delta^*$ resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data with a single free parameter of the model, which was fitted previously by Th. Gutsche to reproduce the axial charge of the Nucleon. However, Nucleon ground state and some of the radially excited baryon resonances (including Roper) are overestimated. Contrary, all the orbitally excited $N^*$ and some of the $\Delta^*$ resonances are underestimated. At the same time, the remaining four Nucleon and five $\Delta$ states including $\Delta(1232)$ are well reproduced. At higher energies, where the experimental data are poor, we can extend our model schematically and predict seven new $N^*$ and four $\Delta^*$ states with larger spin values.

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