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, del(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 similar or equal to 0.137 fm and the spatial extent L-s similar or equal to 4.4 fm with the pion mass m(pi) similar or equal to 530 MeV, the local potentials for two different energies (E similar or equal to 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 similar or equal to 45 MeV are also found to be the same within the errors, which also supports the local approximation.