Reformulation of the pionless effective field theory for practical few- and many-body applications

Abstract

The effective field theory (EFT) of contact forces which describes few-nucleon systems at distance scales larger than the pion Compton wavelength ${\rm EFT}({π\hskip-0.54em /})$ can be defined in terms of momentum-dependent potentials that contain a fixed number of simple poles and generate the effective-range expansion to a given fixed order. These potentials provide a practical generalization of the standard ${\rm EFT}({π\hskip-0.54em /})$ power-counting scheme which, for instance, naturally accounts for the large effective ranges in the s-wave channels. Nucleon-nucleon phase shifts computed in this formulation of ${\rm EFT}({π\hskip-0.54em /})$ are compared to modern phase-shift analyses, and effective-range parameters are tabulated. The ${\rm EFT}({π\hskip-0.54em /})$ potentials, which provide a rational approximation of the S-matrix, are easily extended into the regime of pion physics through the inclusion of additional S-matrix poles and zeros, and provide an accurate description of data up to pion-production threshold. The potentials in this scheme are in an important sense weak over all relevant distance scales, and are therefore of utility for systematic calculations of many-nucleon observables.