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 modelled by its bare part plus a one–loop correction including an effective ∆. 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 renormal-ization. Furthermore, the bare and renormalized pion–nucleon coupling constant are approximately equal, consistent with results from the Cloudy Bag Model.