On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg’s Power Counting

Abstract

Nogga, Timmermans and van Kolck recently argued that Weinberg’s power counting in the few–nucleon sector is inconsistent and requires modifications. Their argument is based on the observed cutoff dependence of the nucleon–nucleon scattering amplitude calculated by solving the Lippmann–Schwinger equation with the regularized one–pion exchange potential and the cutoff Λ varied in the range Λ = 2 . . . 20 fm−1. In this paper we discuss the role the cutoff plays in the application of chiral effective field theory to the two–nucleon system and study carefully the cutoff–dependence of phase shifts and observables based on the one–pion exchange potential. We show that (i) there is no need to use the momentum–space cutoff larger than Λ ~ 3 fm−1; (ii) the neutron–proton low–energy data show no evidence for an inconsistency of Weinberg’s power counting if one uses Λ ~ 3 fm−1.