Divergence Disease of the Pion-Baryon Interaction in Quark-Based Models

We examine the divergence of the baryon self-energy due to the pion-quark interaction in the chiral bag model and the cloudy bag model. For the pion-quark coupling only the lowest nonvanishing (i.e., the second) order is considered but the sum over virtual excitations of the quark is carried out. We point out that there are two types of divergence involved. One is the ultraviolet divergence that is common to local interactions, and the other is peculiar to the bag with a sharp surface. Unlike the former, the latter remains divergent even if the finite size of the pion is taken into account. If the bag surface is smeared and the finite size of the pion is incorporated, the self-energy becomes finite. As far as the question of divergence/convergence of the self-energy is concerned there is no significant difference between the chiral bag and cloudy bag.