T. Mehen and I.W. Stewart, *Nucleon-Nucleon Effective Field Theory at NNLO: Radiation Pions and $^1S_0$ Phase Shift*,
in Proceedings of the INT Workshop on Nuclear Physics with Effective Field Theory, Proc. Inst. Nucl. Theor. 9, edited by P. Bedaque, M. Savage, R. Seki, U. L. Van Kolck
(2000), World Scientific .
**Abstract:**

*Low energy phenomena involving two nucleons can be
successfully described using effective field theory. Because
of the relatively large expansion parameter, it is only at
next-to-next-to-leading order (NNLO) where one can expect to
see agreement with experiment at the few percent level. The
first part of this talk will focus on radiation pion
effects, which first appear at NNLO. The power counting for
radiation pions is simple for center of mass momentum
p~\sqrt{M m_pi}=Q_r, the threshold for pion production. We
explain how graphs calculated with the Q_r power counting
scale for p~m_\pi. The Q_r^3 radiation pion contributions to
nucleon-nucleon scattering are suppressed by inverse powers
of the S-wave scattering lengths. However, we point out that
order Q_r^4 radiation contributions might give a NNLO
contribution for p~m_pi. In the second part of the talk,
results for the potential pion and contact interaction part
of the NNLO 1S0 phase shift are presented. We emphasize the
importance of eliminating spurious poles in the expression
for the amplitude at each order in the perturbative
expansion. Doing this leaves a total of three free
parameters at NNLO. We obtain a good fit to the 1S0 phase
shift.*