Convergence of the self-energy in a relativistic chiral quark model: excited Nucleon and $Δ$ sector

Abstract: A convergence of the valence quark self-energies in the 1S, 2S, $1P_{1/2}$, $1P_{3/2}$ orbits induced by pion and gluon field configurations, is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence, one needs to include contribution of the intermediate quark and anti-quark states with the total momentum up to $j=25/2$. It is argued that a restriction to the lowest mode when estimating the self-energy is not good approximation.