Multipion Systems in Lattice QCD and the Three-Pion Interaction

The ground-state energies of 2, 3, 4, and 5 π⁺'s in a spatial volume V~(2.5 fm)³ are computed with lattice QCD. By eliminating the leading contribution from three-π⁺ interactions, particular combinations of these n-π⁺ ground-state energies provide precise extractions of the π⁺π⁺ scattering length in agreement with that obtained from calculations involving only two π⁺'s. The three-π⁺ interaction can be isolated by forming other combinations of the n-π⁺ ground-state energies. We find a result that is consistent with a repulsive three-π⁺ interaction for m_π352 MeV.