Baryon self-energy due to the pion-quark interaction

We examine the baryon self-energy due to the pion-quark interaction, more specifically, how the self-energy varies among the ground states of the baryon octet and decuplet, and also from the ground to excited states. A nonrelativistic constituent quark model is used in which quarks are bound in a harmonic-oscillator potential. For the excited states we examine the lowest even- and odd-parity states in the nucleon sector. We find that the variation of the self-energy within the same strangeness sector is quite small, i.e., of the order of 30 MeV or smaller. For example, the pion contribution to the Δ-N splitting is ≲20 MeV. In arriving at this small variation it is crucial to take account of the spin dependence of the quark energy that enters in the energy denominator of the self-energy calculation. The individual energy shift is sensitive to the (ad hoc) form factor associated with the pion-quark interaction, and also to the quark excitation in the intermediate state. However, this sensitivity is strongly reduced in the difference between energy shifts for different baryon states.