Isotensor π π π Scattering with a ρ -Resonant Subsystem from QCD

This Letter presents a lattice quantum chromodynamics (QCD) determination of π π π scattering amplitudes for the isospin-2 channel with angular momentum and parity J P = 1 + . The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of m π ≈ 400 MeV , for which the ρ meson manifests as a narrow resonance. The analysis employs a previously developed formalism that nonperturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for π π systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from ≈ 4 / m π to 6 / m π . These combined data constrain the low-lying partial waves of the infinite-volume three-pion K matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.