Pion scattering from quark bag nucleons

The elastic scattering of a pion from quark bag models of the nucleon, the $\Delta \mathrm{}\left(1232\right)\mathrm{}$, and the ${\mathrm{N}}^{*}$ (1470) is investigated. A rank two $\frac{N}{D}$ dispersion theory is used to derive a dynamic equation for pion-nucleon elastic scattering which includes the effect of coupling the pion production channels to the elastic channel. In the limit of no coupling to production channels, the model reduces to the cloudy bag model. In the $P_{11}$ channel, the model is quantitatively in agreement with the experimental phase shifts for pion laboratory kinetic energies below 1 GeV with reasonable parameters. In the $P_{33}$ channel, we find similar quantitative agreement. In this channel, the data allow for any mass of the delta bag greater than about 1290 MeV with the model going over continuously to the Chew-Low model as the mass of the delta bag state is increased. The physical resonance is found to be a mixture of a pion-nucleon Chew-Low—type resonance with the delta state of the bag. A bag radius of approximately 1.1 fm is found but several corrections to the model which would alter this radius are noted.