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

Abstract

We present the solution of the Poincar\'e-covariant Faddeev equation for the $\ensuremath{\Delta}(1232)$ and $\ensuremath{\Omega}(1672)$ 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 nonsphericity of the $\ensuremath{\Delta}$ resonance is discussed as well.