Cloudy bag model, the ‘‘σ’’ meson, andπNscattering

Although the cloudy bag model (CBM) can describe quite well p-wave {π}N scattering it has heretofore been unable to describe the energy dependence of the s-wave phase shifts. This problem is not unique to the CBM; it shows up dramatically in meson-exchange calculations. In this work it is shown that two higher-order graphs in the CBM, which cancel in the soft-pion limit, can cure this problem. One of the two graphs has properties similar to the exchange of a fictitious ``{σ}'' meson and provides long-range attraction. The other term, usually not included in meson-exchange potentials, provides short-range repulsion.