The nuclear force from Monte Carlo simulations of lattice quantum chromodynamics

Abstract

The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of strong interaction, the quantum chromodynamics defined on the hypercubic space–time lattice. After a brief summary of the empirical nucleon–nucleon (NN) potentials that can fit the NN scattering experiments in high precision, we outline the basic formulation for deriving the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe–Salpeter (BS) amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a 324 lattice with lattice spacing a0.137 fm (lattice volume (4.4 fm)4) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at the High Energy Accelerator Research Organization (KEK). We found that the calculated NN potential at low energy has the basic features expected from the empirical NN potentials: attraction at long and medium distances, and the repulsive core at short distances. Various future directions along this line of research are also summarized.