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 th eory. Predictions for the P-1(1), P-3(0,1,2), D-1(2), and D-3(2,3) phase sh ifts at this order are also compared with data. The calculations treat pion s 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 po tential pion exchange which do not vanish in the chiral limit. We compare o ur results to calculations within the Weinberg approach, and find that in s ome spin triplet channels the summation of potential pion diagrams seems to be necessary to reproduce the observed phase shifts. In the spin singlet c hannels the nonperturbative treatment of potential pions does not afford a significant improvement over the perturbative approach. (C) 2000 Elsevier S cience B.V. All rights reserved.