Delta and Omega masses in a three-quark covariant Faddeev approach

TL;DR

This paper solves the covariant Faddeev equation for Delta and Omega baryons, deriving their internal structure and calculating their masses, which align well with experimental data and lattice QCD results, revealing insights into baryon shape.

Contribution

It provides a detailed covariant structure of baryon amplitudes and demonstrates how a rainbow-ladder truncation accurately predicts baryon masses and properties.

Findings

Physical masses agree with experimental data.

Mass evolution matches lattice QCD calculations.

Evidence suggests non-spherical shape of the Delta resonance.

Abstract

We present the solution of the Poincare-covariant Faddeev equation for the Delta(1232) and Omega(1672) baryons. The covariant structure of the corresponding baryon amplitudes and their decomposition in terms of internal spin and orbital angular momentum is explicitly derived. The interaction kernel is truncated to a rainbow-ladder dressed-gluon exchange such that chiral symmetry and its dynamical breaking are correctly implemented. The resulting physical masses agree reasonably with experiment and their evolution with the pion mass compares favorably with lattice calculations. Evidence for the non-sphericity of the Delta-resonance is discussed as well.