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

TL;DR

This paper uses lattice QCD to calculate three-pion scattering amplitudes in the isospin-2 channel, revealing the influence of a $ ho$ resonance at a heavier pion mass, and employs a formalism linking finite-volume spectra to infinite-volume amplitudes.

Contribution

It provides the first lattice QCD determination of three-pion scattering amplitudes with a $ ho$ resonant subsystem in the isospin-2 channel at unphysical pion masses.

Findings

Determined three-pion scattering amplitudes at $m_ eq$ physical mass.

Constrained low-lying partial waves of the three-pion K matrix.

Extracted scattering amplitudes using coupled integral equations.

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 length 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.