Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD

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.