Most applications of the cloudy bag model to πN scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the $P_{11}$ channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ππN system that incorporate three-body unitarity.

• Received 6 March 1986

DOI:https://doi.org/10.1103/PhysRevC.34.991