NNLO corrections to nucleon-nucleon scattering and perturbative pions

The S-1(0), S-3(1), and D-3(1) nucleon-nucleon scattering phase shifts are calculated at next-to-next-to-leading order (NNLO) in an effective field theory. Predictions for the P-1(1), P-3(0,1,2), D-1(2), and D-3(2,3) phase shifts at this order are also compared with data. The calculations treat pions perturbatively and include the NNLO contributions from order Q(r)(3) and Q(r)(4) radiation pion graphs. In the S-3(1), D-3(1) and P-3(0,2) channels we find large disagreement with the Nijmegen partial-wave analysis at NNLO. These spin triplet channels have large corrections from graphs with two potential pion exchange which do not vanish in the chiral limit. We compare our results to calculations within the Weinberg approach, and find that in some spin triplet channels the summation of potential pion diagrams seems to be necessary to reproduce the observed phase shifts. In the spin singlet channels the nonperturbative treatment of potential pions does not afford a significant improvement over the perturbative approach. (C) 2000 Elsevier Science B.V. All rights reserved.