Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

TL;DR

This paper develops a regulator-independent method using dispersion relations and the N/D approach to calculate nucleon-nucleon partial waves from chiral effective field theory, focusing on elastic scattering and one-pion exchange contributions.

Contribution

It introduces a novel application of the N/D method to compute NN partial waves based on dispersion relations, incorporating chiral power counting and constraints for higher angular momentum states.

Findings

Successfully calculated NN partial waves using dispersion relations.

Method is independent of regulator choices.

Applicable to higher orders and coupled partial waves.

Abstract

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller and Meissner [Ann. Phys. (NY) 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum L>=2 is solved in the presence of L-1 constraints, so as to guarantee the right behavior of the D and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.