Eur. Phys. J. A (2017) 53: 83
https://doi.org/10.1140/epja/i2017-12273-x

Regular Article - Theoretical Physics

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

¹ Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany
² Theory Center, Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA
³ Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425, Jülich, Germany
⁴ Department of Physics, North Carolina State University, 27695, Raleigh, NC, USA
⁵ JARA - High Performance Computing, Forschungszentrum Jülich, D-52425, Jülich, Germany

^* e-mail: t.laehde@fz-juelich.de

Received: 27 February 2017
Accepted: 5 April 2017
Published online: 8 May 2017

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 100MeV, the physics of the two-nucleon system is independent of the lattice spacing.