Pions in the Pionless Effective Field Theory

We show that processes involving pions that remain very near their mass-shell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the pion-deuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log(gamma/mpi), where gamma is the deuteron binding momentum, and mpi is the mass of the pion. The coefficient of this logarithm is determined by the S-wave pion-nucleon scattering lengths.