Abstract:
The 1S0, 3S1, and 3D1 nucleon-nucleon scattering phase
shifts are calculated at next-to-next-to-leading order
(NNLO) in an effective field theory. Predictions for the
1P1, 3P0, 3P1, 3P2, 1D2, 3D2, and 3D3 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 3S1,
3D1, 3P0, and 3P2 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.