Renormalization group approach to two-body scattering in the presence of long-range forces

We apply renormalization-group methods to two-body scattering by combination of known long-range and unknown short-range potentials. We impose a cutoff in the basis of distorted waves of the long-range potential and identify possible fixed points of the short-range potential as this cutoff is lowered to zero. The expansions around these fixed points define the power countings for the corresponding effective field theories. Expansions around nontrivial fixed points are shown to correspond to distorted-wave versions of the effective-range expansion. These methods applied to scattering the presence of Coulomb, Yukawa, and repulsive inverse-square potentials.