Relativistic structure of one-meson and one-gluon exchange forces and the lower excitation spectrum of the Nucleon and the Delta

Abstract

The lower excitation spectrum of the nucleon and $\Delta$ is calculated in a relativistic chiral quark model. Corrections to the baryon mass spectrum from the second order self-energy and exchange diagrams induced by pion and gluon fields are estimated in the field -theoretical framework. Convergent results for the self-energy terms are obtained when including the intermediate quark and antiquark states with a total momentum up to $j=25/2$. Relativistic one-meson and color-magnetic one-gluon exchange forces are shown to generate spin 0, 1, 2, etc. operators, which couple the lower and the upper components of the two interacting valence quarks and yield reasonable matrix elements for the lower excitation spectrum of the Nucleon and Delta. The only contribution to the ground state nucleon and $\Delta$ comes from the spin 1 operators, which correspond to the exchanged pion or gluon in the l=1 orbit, thus indicating, that the both pion exchange and color-magnetic gluon exchange forces can contribute to the spin of baryons. Is is shown also that the contribution of the color-electric component of the gluon fields to the baryon spectrum is enormously large (more than 500 MeV with a value ${\alpha }_s=0.65$) and one needs to restrict to very small values of the strong coupling constant or to exclude completely the gluon-loop corrections to the baryon spectrum. With this restriction, the calculated spectrum reproduces the main properties of the data, however needs further contribution from the two-pion exchange and instanton induced exchange (for the nucleon sector) forces in consistence with the realistic NN-interaction models.

arXiv comment15 pages, 4 figures, 7 tables

References in corpus (16)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics
• Unified description of light- and strange-baryon spectra
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces I. The non-strange baryon spectrum and ground-states
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces II. The strange baryon spectrum
• Relativistic quark models of baryons with instantaneous forces
• Effective Q-Q Interactions in Constituent Quark Models
• Electromagnetic Form Factors of the Nucleon in an Improved Quark Model
• Resolution of the Proton Spin Problem
• Two-Pion Exchange Interaction Between Constituent Quarks
• Quark-meson coupling model with the cloudy bag
• Beyond the Adiabatic Approximation: the impact of thresholds on the hadronic spectrum
• The Spin of the Proton
• Ground-state baryon masses in the perturbative chiral quark model
• Lower Excitation Spectrum of the Nucleon and Delta in a Relativistic Chiral Quark Model

Cited by in corpus (2)

• Spectrum of the excited $N^{\ast }$ and ${\Delta }^{\ast }$ baryons in a relativistic chiral quark model
• Convergence of the self-energy in a relativistic chiral quark model: excited Nucleon and $\Delta$ sector