Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction

TL;DR

This study uses lattice QCD to compute energies of multi-pion systems, extracting scattering lengths and three-pion interactions, revealing a repulsive three-pion interaction at certain pion masses.

Contribution

It introduces a method to isolate and analyze three-pion interactions in lattice QCD, providing new insights into multi-pion dynamics.

Findings

Ground-state energies computed for 2-5 pions.

Precise extraction of +scattering length.

Evidence of repulsive three-+interaction for m_\u03c0 < 352 MeV.

Abstract

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.