Lower Excitation Spectrum of the Nucleon and Delta in a Relativistic Chiral Quark Model

Abstract

The lower excitation spectrum of the nucleon and $\Delta$ is calculated in a relativistic chiral quark model. Contributions of the second order self-energy and exchange diagrams due-to pion fields to the mass spectrum of the SU(2) baryons are estimated. A splitting between N(939) and positive parity nucleon resonance (Roper resonance) $N^{\ast }(1440)$ is reproduced with a reasonable accuracy. The obtained structure of one-meson exchange interaction confirms a prediction of the large $N_c$ limit approach stating that the mass splitting between various baryon states receive contributions from operators which simultaneously couple spin, isospin and orbital momentum. It is shown that one-meson exchange interaction generates a splitting between negative parity $N^{\ast }(1/2^{-})$ and $N^{\ast }(3/2^{-})$ states, and also between ${\Delta }^{\ast }(3/2^{-})$ and ${\Delta }^{\ast }(1/2^{-})$ states in contrast to the non-relativistic Goldstone-Boson Exchange based quark models. This splitting is due-to a relativistic operator which couples the lower and upper orbital momentum of two interacting valence quarks.

Comments: 11 pages, 2 figures, 6 tables; replaced with revised version