Nuclear Force from Lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the nuclear force, specifically the nucleon-nucleon potential, revealing a repulsive core at short distances and demonstrating the method's promise for future studies.

Contribution

It introduces a lattice QCD method to reconstruct the NN potential from the Bethe-Salpeter wave function, providing new insights into nuclear forces from first principles.

Findings

The NN potential exhibits a clear repulsive core of about 500 MeV at short distances.

The method faithfully reproduces the NN potential consistent with experimental scattering data.

The approach shows promise for future lattice QCD studies of nuclear interactions.

Abstract

The first lattice QCD result on the nuclear force (the NN potential) is presented in the quenched level. The standard Wilson gauge action and the standard Wilson quark action are employed on the lattice of the size 16^3\times 24 with the gauge coupling beta=5.7 and the hopping parameter kappa=0.1665. To obtain the NN potential, we adopt a method recently proposed by CP-PACS collaboration to study the pi pi scattering phase shift. It turns out that this method provides the NN potentials which are faithful to those obtained in the analysis of NN scattering data. By identifying the equal-time Bethe-Salpeter wave function with the Schroedinger wave function for the two nucleon system, the NN potential is reconstructed so that the wave function satisfies the time-independent Schroedinger equation. In this report, we restrict ourselves to the J^P=0^+ and I=1 channel, which enables us to pick up unambiguously the ``central'' NN potential V_{central}(r). The resulting potential is seen to posses a clear repulsive core of about 500 MeV at short distance (r < 0.5 fm). Although the attraction in the intermediate and long distance regions is still missing in the present lattice set-up, our method is appeared to be quite promising in reconstructing the NN potential with lattice QCD.