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

TL;DR

This paper combines chiral effective field theory with dispersion relations to analyze two-nucleon scattering near threshold, achieving accurate phase shifts and supporting perturbative calculations of nucleon-nucleon interactions.

Contribution

It introduces a method that merges chiral perturbation theory with dispersion relations for improved two-nucleon scattering analysis near threshold.

Findings

Accurate description of empirical S- and P-wave phase shifts.

Good convergence of the theoretical approach.

Supports perturbative computation of subthreshold nucleon-nucleon amplitudes.

Abstract

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 $T_{{\rm lab}}\simeq250$ 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.