The ground-state energies of 2, 3, 4 and 5 \pi^+'s in a spatial volume V (2.5 fm)^3 are computed with lattice QCD. By eliminating the leading contribution from three-\pi^+ interactions, particular combinations of these n-\pi^+ ground-state energies provide precise extractions of the \pi^+\pi^+ scattering length in agreement with that obtained from calculations involving only two \pi^+'s. The three-\pi^+ interaction can be isolated by forming other combinations of the n-\pi^+ ground-state energies. We find a result that is consistent with a repulsive three-\pi^+ interaction for m_\pi < 352 MeV.
@article{arxiv.0710.1827,
title = {Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction},
author = {Silas R. Beane and William Detmold and Thomas C. Luu and Kostas Orginos and Martin J. Savage and Aaron Torok},
journal= {arXiv preprint arXiv:0710.1827},
year = {2014}
}