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An 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 $m_π/m_ρ\approx 0.73-0.95$. 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 $π$-$N$ and $π$-$π$ cases, a trend which is qualitatively consistent with the experiment. Problems toward a more realistic calculation for light quarks are discussed.