Nucleon-nucleon scattering from dispersion relations: Next-to-next-to-leading order study

Abstract

Nucleon-nucleon $(\mathit{NN})$ scattering is studied by applying an approach based on the $\mathit{N}/\mathit{D}$ method and chiral perturbation theory (ChPT), whose dynamical input per partial wave consists of the imaginary part of the $\mathit{NN}$ partial-wave amplitude along the left-hand cut. The latter is calculated in one-loop ChPT up to and including next-to-next-to-leading order (NNLO). A power counting for the subtraction constants is established, which is appropriate for those subtractions attached to both the left- and the right-hand cuts. A quite good reproduction of the Nijmegen partial-wave analysis phase shifts and mixing angles results, which implies a steady improvement in the accurateness achieved by increasing the chiral order in the calculation of the dynamical input. I discuss that it is not necessary to fine tune the chiral counterterms ${c}_{i}$ determined from pion-nucleon scattering to agree with $\mathit{NN}$ data, but instead one should perform the iteration of two-nucleon intermediate states in a well-defined way so as to keep proper unitarity and analyticity. It is also confirmed at NNLO the long-range correlations between the $\mathit{NN} S$-wave effective ranges and scattering lengths, when employing only once-subtracted dispersion relations, that hold up to around 10% when compared with experimental values.