Non-locality of the nucleon-nucleon potential from Lattice QCD

TL;DR

This study investigates the non-locality of the nucleon-nucleon potential derived from lattice QCD, finding that non-locality and angular momentum dependence are negligible at low energies, supporting the use of derivative expansion.

Contribution

It provides an analysis of the non-locality and angular momentum dependence of NN potentials from lattice QCD, validating the derivative expansion approach at low energies.

Findings

Non-locality is negligible within statistical errors.

Angular momentum dependence is negligible at low energies.

Potential convergence is supported by the results.

Abstract

The Nambu-Bethe-Salpeter (NBS) wave function for two nucleons on the lattice has been shown to yield a non-local and energy-independent nucleon-nucleon (NN) potential, U(r,r'). In practice, the derivative expansion of U(r,r') is currently employed to determine the potential at low energies. In this report, we study the magnitude of non-locality to check the convergence of such a derivative expansion. With quenched lattice QCD at m_\pi = 530MeV, we compare the NN potentials at the center of mass energy E ~ 0 MeV and at E ~ 45 MeV. We also investigate the angular momentum dependence of the spin singlet potential, by comparing the potentials in 1S0 and 1D2 channels. We find that the non-locality and the angular momentum dependence in the above energy range are negligible within statistical errors.