# Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

## TL;DR

This paper systematically studies neutron-proton scattering using Nuclear Lattice Effective Field Theory up to NNLO, demonstrating small lattice artifacts at fine lattice spacings and good agreement with experimental phase shifts.

## Contribution

It provides a non-perturbative NNLO analysis of neutron-proton scattering in NLEFT with a radial Hamiltonian method, including uncertainty estimates and lattice artifact assessments.

## Key findings

- NNLO results agree with Nijmegen partial-wave analysis at a = 0.98 fm
- Lattice artifacts are small at finer lattice spacings
- Physics below 100 MeV CM momentum is lattice-spacing independent

## Abstract

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.