Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

TL;DR

This paper develops a dispersion relation-based method for analyzing nucleon-nucleon interactions in coupled partial waves using chiral effective field theory, extending previous work to include coupled channels and focusing on the deuteron pole.

Contribution

It extends the N/D method to coupled partial waves in nucleon-nucleon interactions within chiral EFT, including the treatment of the deuteron pole and unitarity constraints.

Findings

Successfully applied the method to leading order one-pion exchange

Derived coupled-channel dispersion relations independent of regulators

Provided a systematic framework for higher-order improvements

Abstract

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.