Covariant solution of the three-quark problem in quantum field theory: the nucleon

TL;DR

This paper presents a detailed covariant solution to the three-quark problem in quantum field theory, specifically focusing on the nucleon, using a Poincare-covariant approach and rainbow-ladder kernel for comparison with other models.

Contribution

It introduces a comprehensive covariant Faddeev equation solution for the nucleon with explicit three-quark structure and detailed amplitude construction, enabling comparison with meson and diquark models.

Findings

First numerical results for the nucleon's amplitude are discussed.

The covariant three-quark amplitude is constructed and compared to existing notations.

The approach allows for consistent comparison with meson and baryon studies.

Abstract

We provide details on a recent solution of the nucleon's covariant Faddeev equation in an explicit three-quark approach. The full Poincare-covariant structure of the three-quark amplitude is implemented through an orthogonal basis obtained from a partial-wave decomposition. We employ a rainbow-ladder gluon exchange kernel which allows for a comparison with meson Bethe-Salpeter and baryon quark-diquark studies. We describe the construction of the three-quark amplitude in full detail and compare it to a notation widespread in recent publications. Finally, we discuss first numerical results for the nucleon's amplitude.