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

TL;DR

This paper demonstrates the convergence of valence quark self-energies in a relativistic chiral quark model for excited nucleon and delta states, emphasizing the importance of including high angular momentum intermediate states.

Contribution

It shows that including intermediate quark and anti-quark states up to j=25/2 is necessary for self-energy convergence in a relativistic chiral quark model.

Findings

Self-energies converge when high angular momentum states are included.

Restriction to lowest modes is insufficient for accurate self-energy estimation.

High angular momentum states significantly impact the self-energy calculations.

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.