Mesonic cloud contribution to the nucleon and delta masses

Pion-nucleon elastic scattering in the dominant P33 channel is examined in the model in which the interaction is of the form π + N ↔ N, ∆(1232). A Low equation formalism is employed which uses covariant phase space and normalizations, a finite nucleon mass, and generates the invariant scattering amplitude which is free of kinematic singularities. New expressions are found for the elastic pion-nucleon scattering amplitude which differ from existing formula both in the kinematics and in the treatment of the renormalization of the nucleon mass and coupling constant. Fitting the model to the phase shifts in the P33 channel does not uniquely fix the parameters of the model. The cutoff for the pion-nucleon form factor is found to lie in the range β = 750±350 MeV/c. The masses of the nucleon and the ∆ which would arise if there were no coupling to mesons are found to be m(0) N = 1179 ± 218 MeV and m (0) ∆ = 1491 ± 198 MeV. The difference in these bare masses, a quantity which would be accounted for by a residual gluon interaction, is found to be δm(0) = 341 ± 116 MeV. 14.20.Dh, 25.80.Dj, 13.75.Gx Typeset using REVTEX