Effect ofππinteractions inπN scattering

The standard cloudy bag model description of πN scattering is extended to include contributions at the two-pion level. The ππ scattering amplitudes are parametrized in phenomenological, separable forms consistent with the known ππ S- and P-wave phase shifts. These amplitudes are embedded in the πN description to account for scattering of the incident pion from the nucleon’s virtual pion cloud. A self-consistent analysis of the coupled πN, πΔ, and π${\mathrm{N}}^{\mathrm{*}}$ (1470) systems results in excellent reproduction of the phase shifts in the πN $P_{33}$ channel to energies above the pion production threshold. In the $P_{11}$ channel, without two-pion intermediate states, no acceptable fit to the data is possible for any values of the bag parameters. It is shown that the additional attraction provided by ππ scattering is essential to reproduce the low-energy phase shifts and fix the sign change at the correct energy.