Two-nucleon scattering: Merging chiral effective field theory with dispersion relations

We consider two-nucleon scattering close to threshold. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes calculated in a relativistic formulation of chiral perturbation theory. The constraints set by unitarity are used in order to stabilize the extrapolation. Neutron-proton phase shifts are analyzed up to laboratory energies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{lab}\simeq 250$\end{document} MeV based on the next-to-next-to-next-to-leading order expression for the subthreshold amplitudes. We find a reasonably accurate description of the empirical S- and P-waves and a good convergence of our approach. These results support the assumption that the subthreshold nucleon-nucleon scattering amplitude may be computed perturbatively by means of the chiral expansion. The intricate soft scales that govern the low-energy nucleon-nucleon scattering are generated dynamically via a controlled analytic continuation.