Next-to-next-to-leading-order calculation of two-nucleon scattering in an effective field theory - art. no. 054004

We use effective field theory (EFT) to calculate the nucleon-nucleon scatte ring amplitude up to next-to-next-to-leading order (NNLO), where we include instantaneous pion exchange but ignore retardation effects. The scattering amplitude in the S-1(0) channel is calculated using the Kaplan-Savage-Wise power counting scheme. An expansion of the amplitude about the pole at low (imaginary momentum is used to derive matching conditions for the EFT coup lings. After imposing constraints from a renormalization group flow analysi s, there are no new free parameters in the amplitude at NNLO. We apply the calculation to a toy model in which there is only instantaneous pion exchan ge by construction, namely, the two-Yukawa model. We find that, through nex t-to-next-to-leading order, each successive tel-m in the low energy expansi on does systematically improve the approximation to the full amplitude. [S0 556-2813(99)01811-7].