Hadron interactions from lattice QCD

Studies on hadron interactions from lattice QCD are reviewed. The S-wave ππ scattering lengths of the I = 0 and I = 2 channels are extracted from various lattice determinations of low energy constants in N f = 2 chiral perturbation theory. The results agree with each other and agree also with other non-lattice estimates. Recently the P-wave ππ scattering phase shift for the I = 1 channel has been calculated. A preliminary estimate of the ρ meson decay width from the phase shift is consistent with the experimental value. Two approaches to potentials between hadrons are discussed. One is a method using static quarks to define the distance between two hadrons. The other is a method to define a potential from a wave function of two hadrons. An application of the latter to the nucleon-nucleon (NN) potential turns out to reproduce qualitative features of the phenomenological NN potential such as attraction at long distance and repulsion at short distance. Theoretical issues of this approach are also discussed.