Isotensor $\pi \pi \pi$ scattering with a $\rho$ resonant subsystem from QCD

Abstract

This work presents a lattice quantum chromodynamics (QCD) determination of $\pi \pi \pi$ 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 $m_{\pi }\approx 400$~MeV, for which the $\rho$ meson manifests as a narrow resonance. The analysis employs a previously developed formalism that non-perturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for $\pi \pi$ 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 lengths ranging from $\approx 4/m_{\pi }$ to $6/m_{\pi }$. 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.

arXiv comment26 pages, 10 figures; the final version includes revisions to the introduction, outlook, acknowledgments, and references, and is updated to be consistent with the published version in Phys. Rev. Lett. 137, 111901 (2026)