Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study

TL;DR

This study applies the dispersive N/D method to nucleon-nucleon interactions using chiral effective field theory, demonstrating improved phase shift predictions and establishing correlations between scattering parameters.

Contribution

It introduces a novel application of the N/D method at next-to-leading order with chiral inputs, improving upon previous models for NN scattering.

Findings

Phase shifts are well reproduced with the method.

The integral equation has a unique solution for OPE input.

Discontinuities are compatible with chiral expansion.

Abstract

We consider nucleon-nucleon ($NN$) interactions from Chiral Effective Field Theory applying the $N/D$ method. The dynamical input is given by the discontinuity of the $NN$ partial-wave amplitudes across the left-hand cut (LHC) calculated in Chiral Perturbation Theory (ChPT) by including one-pion exchange (OPE), once-iterated OPE and leading irreducible two-pion exchange (TPE). We discuss both uncoupled and coupled partial-waves. We show algebraically that the resulting integral equation has a unique solution when the input is taken only from OPE because it is of the Fredholm type with a squared integrable kernel and an inhomogeneous term. Phase shifts and mixing angles are typically rather well reproduced, and a clear improvement of the results obtained previously with only OPE is manifest. We also show that the contributions to the discontinuity across the LHC are amenable to a chiral expansion. Our method also establishes correlations between the $S$-wave effective ranges and scattering lengths based on unitarity, analyticity and chiral symmetry.