Two of recent progress in lattice QCD approach to nuclear force are reported. (i) Tensor force from quenched lattice QCD: By truncating the derivative expansion of inter-nucleon potential to the strictly local terms, we obtain central force V_C(r) an
d tensor force V_T(r) separately from s-wave and d-wave components of Bethe-Salpeter wave function for two nucleon state with J^P=1^+. Numerical calculation is performed with quenched QCD on 32^4 lattice using the standard plaquette action at beta=5.7 with the standard Wilson quark action with kappa=0.1640, 0.1665, 0.1678. Preliminary results show that the depths of the resulting tensor force amount to 20 to 40 MeV, which is enhanced in the light quark mass region. (ii) Nuclear force from 2+1 flavor QCD with PACS-CS gauge configuration: Preliminary full QCD results are obtained by using 2+1 flavor gauge configurations generated by PACS-CS collaboration. The resulting potential has the midium range attraction of about 30 MeV similar to the preceding quenched calculations. However, the repulsive core at short distance is significantly stronger than the corresponding quenched QCD result.
We present our updated results of the nucleon-nucleon potential in quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on the 32^4(simeq (4.4 fm)^4) lattice. From the equal-time Bethe-Salpeter (BS) wave functi
on, the NN potential is constructed through the Schroedinger-type equation. Resulting NN potential has all the qualitative features which phenomenological potentials commonly have: the repulsive core at short distance and the attractive well at medium and long distances. In the L to infty limit, our NN potential is guaranteed to reproduce the scattering length obtained from the Lueschers formula. The quark mass dependence of the NN potential is studied with m_{pi} sim 380, 529, 731 MeV. The results suggest that both the repulsive core at short distance and the attractive well at medium distance are enhanced in the light quark mass region.
