Coupled-channel approach to isotensor $\pi\pi\pi$ scattering from lattice QCD

TL;DR

This paper develops a coupled-channel approach to analyze three-pion systems with isospin 2 using lattice QCD, providing insights into three-body dynamics and resonance behavior from first principles.

Contribution

It introduces a generalized finite-volume three-body quantization condition for coupled channels and applies it to lattice QCD data at different pion masses, advancing the understanding of three-body interactions.

Findings

Finite-volume spectra computed at two pion masses.

Mapping of lattice data to infinite-volume amplitudes.

Comparison with effective Lagrangian predictions.

Abstract

The quest to understand three-body dynamics from first-principle QCD includes the study of non-resonant and resonant systems. The isospin $I=2$ system is of particular interest having no three-body resonance but featuring a resonance in a sub-channel, while also being a coupled-channel problem. In this study, we calculate the finite-volume spectrum from lattice QC at two different pion masses, map the amplitude to the infinite volume through a generalized FVU three-body quantization condition, investigate the limit of a narrow $\rho$, and compare with an effective Lagrangian prediction at leading order. Chiral extrapolations between different pion masses are performed.