Neutron-deuteron scattering revisited with the EKM chiral nuclear force and the WPCD method

TL;DR

This study revisits neutron-deuteron scattering using advanced chiral nuclear forces and a novel computational method, confirming previous findings and highlighting the persistent $A_y$ puzzle despite improved theoretical models.

Contribution

The paper introduces a direct solution of Faddeev-AGS equations with the WPCD method and EKM chiral forces, avoiding pseudo-states and enabling potential relativistic extensions.

Findings

Differential cross sections are well described up to N$^3$LO.

The $A_y$ puzzle remains unresolved at N$^3$LO.

Results with EKM and Idaho N$^3$LO forces are consistent.

Abstract

We revisit the neutron-deuteron scattering using the Wave-Packet Continuum Discretization (WPCD) method with the EKM chiral nuclear force at various chiral orders. We rederive the permutation operator and solve the Faddeev-AGS equations directly, without rewriting the initial Faddeev kernel $tG_0$ and introducing pseudo-states, thereby rendering the approach easily extendable to a relativistic framework. We find that up to the next-to-next-to-next-to-leading order (N$^3$LO), although one can well describe the differential cross sections, one cannot resolve the long-standing $A_y$ puzzle, consistent with previous studies. The fact that the N$^3$LO chiral forces can well describe the $NN$ phase shifts and the results obtained with the EKM and Idaho N$^3$LO chiral forces agree with each other underscores the need for further investigations to resolve the $A_y$ puzzle, e.g., considering three-body forces or relativistic effects.