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 Lambda varied in the range Lambda = 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 Lambda ~ 3 fm^(-1); (ii) the neutron-proton low-energy data show no evidence for an inconsistency of Weinberg's power counting if one uses Lambda ~ 3 fm^{-1}.

15 pages, 12 figures, updated and published version

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• Power counting with one-pion exchange
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• Renormalization of the Deuteron with One Pion Exchange
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• Isospin-violating nucleon-nucleon forces using the method of unitary transformation

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