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

Abstract

We provide details on a recent solution of the nucleon’s covariant Faddeev equation in an explicit three-quark approach. The full Poincaré-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.