Energy dependence of nucleon-nucleon potentials

TL;DR

This paper studies how nucleon-nucleon potentials depend on energy, showing weak energy dependence at low energies through analytical and numerical methods in quantum field theories.

Contribution

It provides the first combined analytical and numerical analysis of energy dependence of nucleon-nucleon potentials in quantum field theories.

Findings

Weak energy dependence of potentials at low energies.

Potentials are nearly identical at 0 and 50 MeV energies.

Analytical evaluation in 2D Ising field theory supports numerical results.

Abstract

We investigate the energy dependence of potentials defined through the Bethe-Salpeter wave functions. We analytically evaluate such a potential in the Ising field theory in 2 dimensions and show that its energy dependence is weak at low energy. We then numerically calculate the nucleon-nucleon potential at non-zero energy using quenched QCD with anti-periodic boundary condition. In this case we also observe that the potentials are almost identical at $E\simeq 0$ and $E\simeq 50$ MeV, where $E$ is the center of mass kinetic energy.