Baryonic Bound States in the Non-Local NJL Model

TL;DR

This paper discusses a covariant, non-local NJL model approach to baryons as three-quark bound states, using a quark-diquark Bethe-Salpeter framework to compute baryon properties.

Contribution

It reformulates baryonic bound states within a non-local NJL model using a relativistic Faddeev approach and quark-diquark Bethe-Salpeter equations, inspired by QCD considerations.

Findings

Baryon masses and form factors can be extracted from coupled integral equations.

The non-local NJL model provides a compact, QCD-motivated framework.

The approach reduces the three-quark problem to an effective quark-diquark bound-state problem.

Abstract

Baryons, as three-quark bound states, require a covariant treatment in the intermediate-energy regime where perturbative QCD is no longer applicable and where nonperturbative correlations dominate. This article reformulates the content of the CERN Baltic Conference 2025 presentation on baryonic bound states in the non-local Nambu--Jona-Lasinio (NJL) model. We review how the relativistic Faddeev approach reduces the three-body quark problem to an effective quark--diquark bound-state problem, describe the scalar and axial-vector diquark channels, and show how the resulting quark--diquark Bethe--Salpeter equation can be written as an eigenvalue problem for the baryon mass. The non-local NJL framework, motivated by QCD-based nonlocal interactions and Dyson--Schwinger considerations, provides a compact description in which baryon masses and form factors are extracted from the numerical solution of coupled integral equations.