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 π-N and π-π scattering lengths are also calculated for comparison. The calculations are made with heavy quarks corresponding to mπ/mρ ≈ 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 π-N and π-π cases, a trend which is qualitatively consistent with the experiment. Problems toward a more realistic calculation for light quarks are discussed.