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

TL;DR

This paper models the lower excitation spectrum of nucleons and Delta particles using a relativistic chiral quark framework, incorporating pion and gluon exchange forces, and discusses their impact on baryon spin and spectrum accuracy.

Contribution

It introduces a relativistic approach to baryon spectrum calculations including pion and gluon exchanges, highlighting the significance of spin operators and the effects of gluon field components.

Findings

Relativistic exchange forces generate spin operators affecting baryon excitation states.

Color-electric gluon contributions are large, requiring small coupling constants or exclusion of gluon loops.

Spectrum aligns with data when considering additional two-pion and instanton-induced forces.

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.