Regularization Methods for Nucleon-Nucleon Effective Field Theory

Attempts to apply effective field theory (EFT) methods to nonrelativistic nucleon-nucleon (NN) scattering have raised questions about the nature and limitations of an EFT expansion when used nonperturbatively. We discuss the characteristics of a meaningful EFT analysis and compare them with traditional approaches to NN scattering. A key feature of an EFT treatment is a systematic expansion in powers of momentum, which we demonstrate using an error analysis introduced by Lepage. A clear graphical determination of the radius of convergence for the momentum expansion is also obtained. We use these techniques to compare cutoff regularization, two forms of dimensional regularization, and the dibaryon approach, using a simple model for illustration. The naturalness of the parameters and predictions for bound-state energies are also shown.