Nucleon mass and pion loops: Renormalization

Using Dyson-Schwinger equations, the nucleon propagator is analyzed nonperturbatively in a field-theoretical model for the pion-nucleon interaction. Infinities are circumvented by using pion-nucleon form factors which define the physical scale. It is shown that the correct, finite, on-shell nucleon renormalization is important for the value of the mass shift and the propagator. For physically acceptable forms of the pion-nucleon form factor the rainbow approximation together with renormalization is inconsistent. Going beyond the rainbow approximation, the full pion-nucleon vertex is modeled by its bare part plus a one-loop correction including an effective $\ensuremath{\Delta}.$ It is found that a consistent value for the nucleon mass shift can be obtained as a consequence of a subtle interplay between wave function and vertex renormalization. Furthermore, the bare and renormalized pion-nucleon coupling constants are approximately equal, consistent with results from the cloudy bag model.