An Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD

TL;DR

This study explores nucleon-nucleon scattering lengths using quenched lattice QCD with heavy quarks, revealing attractive forces consistent with experimental trends, and compares these with pion-nucleon and pion-pion scattering lengths.

Contribution

It provides the first lattice QCD calculations of nucleon-nucleon scattering lengths with heavy quarks, highlighting the attractive nature of the force and discussing challenges for lighter quark simulations.

Findings

N-N system exhibits attractive force in both spin channels

Scattering lengths are larger than those for π-N and π-π

Results qualitatively agree with experimental observations

Abstract

An exploratory study is made of the nucleon-nucleon $s$-wave scattering lengths in quenched lattice QCD with the Wilson quark action. The $\pi$-$N$ and $\pi$-$\pi$ scattering lengths are also calculated for comparison. The calculations are made with heavy quarks corresponding to $m_\pi/m_\rho\approx 0.73-0.95$. The results show that the $N$-$N$ system has an attractive force in both spin-singlet and triplet channels, with their scattering lengths significantly larger than those for the $\pi$-$N$ and $\pi$-$\pi$ cases, a trend which is qualitatively consistent with the experiment. Problems toward a more realistic calculation for light quarks are discussed.