Baryon self-energies due to pion-quark coupling

Pionic self-energy contributions to the nucleon and Δ are calculated perturbatively in the nonrelativistic constituent-quark model. The intermediate states are not restricted to the ground states of N and Δ. The difference in the self-energies of nucleon and Δ ground states converges satisfactorily, and may give rise to appreciable splitting if the hyperfine splitting from gluon exchange is less than 200 MeV. The results are very sensitive to the assumed axial size of the nucleon. For an axial radius of about 0.6 fm, the pionic self-energy contribution to the N-Δ splitting is approximately the same as found from the one-pion-exchange potential model. The difference in the pionic self-energies of the odd-parity excited states and the ground state is found to converge too slowly to make any definite statements