Nucleon-Nucleon Potential and its Non-locality in Lattice QCD

TL;DR

This study uses quenched lattice QCD simulations to examine the nucleon-nucleon potential's non-locality, validating the local approximation up to 45 MeV for various energies and angular momenta.

Contribution

It demonstrates that the nucleon-nucleon potential can be approximated locally up to 45 MeV, supporting the derivative expansion approach in lattice QCD calculations.

Findings

Local potentials at different energies are statistically identical.

Central potentials for different angular momenta are consistent within errors.

The local approximation of the potential is valid up to 45 MeV.

Abstract

By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) \delta^3(r-r') is studied. The relative kinetic energy between two nucleons is introduced through the anti-periodic boundary condition in the spatial directions. On a hypercubic lattice with the lattice spacing a ~ 0.137 fm and the spatial extent L_s ~ 4.4 fm with the pion mass m_{\pi} ~ 530 MeV, the local potentials for two different energies (E ~ 0 MeV and 45 MeV) are compared and found to be identical within statistical errors, which validates the local approximation of U(r,r') up to E=45 MeV for the central and tensor potentials. Central potentials in the spin-singlet channel for different orbital angular momentums (l=0 and l=2) at E ~ 45 MeV are also found to be the same within the errors, which also supports the local approximation.