Nucleon-Nucleon Potential and Its Non-Locality in Lattice QCD

By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the derivative expansion of the general nucleon-nucleon potential U(r,r′) = V(r, ∇r) δ3(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 Ls ≃ 4.4 fm with the pion mass mπ ≃ 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.