Low equation, pion-nucleon scattering, and Castillejo-Dalitz-Dyson pole

We examine the p-wave πN scattering at medium energies by means of the Low equation with a view to determining the form factor of the πN interaction. Solutions of the equation with and without a Castillejo-Dalitz-Dyson (CDD) pole are used. The solution with no CDD pole corresponds to the old Chew-Low model, whereas the one with a CDD pole corresponds to the quark version of the Chew-Low model. The πN interaction form factor is determined so that the Δ resonance is well reproduced. We find that the solution with a CDD pole leads to a softer form factor but is not as soft as those expected from the nucleon size in the quark model. Using the solutions and form factors thus determined, we also examine the pionic contributions to the nucleon magnetic moment and the nucleon mass