Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD

Abstract

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