Lattice Nuclear Force

We derive an energy-independent and non-local potential for the baryon-baryon interaction from the Nambu-Bethe-Salpeter amplitude on the lattice. The method is applied to the nucleon-nucleon interactions with the (2+1)-flavor lattice QCD simulations. The central and tensor potentials are obtained as leading order terms of the velocity expansion of the non-local potential: The central potential has a repulsive core surrounded by an attractive well, while the tensor potential has intermediate and long range attractions. Validity of the velocity expansions tested by the nucleon-nucleon interaction with finite relative momentum. Interactions among octet-baryons in the flavor SU(3) limit are also studied in full QCD simulations to unravel the origin of the repulsive core and the possible existence of $H$-dibaryon.

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