Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics

TL;DR

This paper uses lattice QCD Monte Carlo simulations to derive the nucleon-nucleon potential, revealing features like attraction and repulsion consistent with empirical models, advancing understanding of nuclear forces from fundamental theory.

Contribution

It presents a novel lattice QCD approach to calculate the nuclear force, connecting fundamental quark-gluon interactions to nucleon-nucleon potentials.

Findings

NN potential shows attraction at long/medium distances

Repulsive core observed at short distances

Results align with empirical NN potentials

Abstract

The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of the strong interaction, the quantum chromodynamics defined on the hypercubic space-time lattice. After a brief summary of the empirical nucleon-nucleon (NN) potentials which can fit the NN scattering experiments in high precision, we outline the basic formulation to derive the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe-Salpeter amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a $32^4$ lattice with the lattice spacing $a \simeq 0.137 $fm (lattice volume (4.4 fm)$^4$) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at KEK. We found that the calculated NN potential at low energy has basic features expected from the empirical NN potentials; attraction at long and medium distances and the repulsive core at short distance. Various future directions along this line of research are also summarized.