<i>Ab initio</i> lattice study of neutron–alpha scattering with chiral forces at N3LO

Abstract We present the first ab initio lattice calculation of neutron–alpha ( n – α ) scattering using nuclear lattice effective field theory with chiral interactions at next-to-next-to-next-to-leading order (N3LO). Building on the high-fidelity chiral Hamiltonian introduced in Elhatisari et al (2024 Nature 630 59), we compute scattering phase shifts in the S - and P -wave channels using the Lüscher finite-volume method. Our results demonstrate excellent agreement with empirical R -matrix phase shifts in the 2 S 1/2 and 2 P 3/2 channels, while revealing persistent discrepancies in the 2 P 1/2 channel for neutron energies above 5 MeV. To systematically investigate these discrepancies, we construct and analyze a simplified neutron–alpha toy model, demonstrating that these discrepancies are not due to the use of the Lüscher finite-volume method. Additionally, we revisit our three-nucleon (3N) force fitting procedure, explicitly incorporating neutron–alpha scattering data through comprehensive Markov Chain Monte Carlo sampling. This analysis confirms the stability of nuclear binding-energy predictions and highlights the need for further refinements in the lattice N3LO three-nucleon forces to fully describe neutron–alpha scattering in the challenging 2 P 1/2 channel.