The light baryon spectrum in a relativistic quark model with instanton-induced quark forces I. The non-strange baryon spectrum and ground-states

TL;DR

This paper develops a relativistic quark model to analyze the non-strange baryon spectrum, demonstrating that instanton-induced forces and relativistic effects can explain key features like the Roper resonance and parity doublets.

Contribution

It introduces a covariant Bethe-Salpeter framework with instanton-induced interactions to accurately describe light baryon spectra, favoring 't Hooft's force over one-gluon exchange.

Findings

Successfully reproduces non-strange baryon spectrum features

Explains Roper resonance and parity doublets through relativistic effects

Demonstrates the importance of instanton-induced forces in baryon structure

Abstract

This is the second of a series of three papers treating light baryon resonances up to 3 GeV within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we apply the covariant Salpeter framework (which we developed in the first paper) to specific quark model calculations. Quark confinement is realized by a linearly rising three-body string potential with appropriate spinorial structures in Dirac-space. To describe the hyperfine structure of the baryon spectrum we adopt 't Hooft's residual interaction based on QCD-instanton effects and demonstrate that the alternative one-gluon-exchange is disfavored phenomenological grounds. Our fully relativistic framework allows to investigate the effects of the full Dirac structures of residual and confinement forces on the structure of the mass spectrum. In the present paper we present a detailed analysis of the complete non-strange baryon spectrum and show that several prominent features of the nucleon spectrum such as e.g. the Roper resonance and approximate ''parity doublets'' can be uniformly explained due to a specific interplay of relativistic effects, the confinement potential and 't Hooft's force. The results for the spectrum of strange baryons will be discussed in a subsequent paper.