Three-pion scattering: From the chiral Lagrangian to the lattice

TL;DR

This paper derives the next-to-leading order three-pion scattering amplitude in chiral perturbation theory and connects it to lattice QCD results, improving the agreement between theoretical predictions and numerical simulations.

Contribution

It provides the first next-to-leading order calculation of three-pion scattering amplitude in chiral perturbation theory and its conversion to the three-particle K-matrix for lattice comparison.

Findings

Enhanced agreement between theory and lattice data.

Improved understanding of multi-meson dynamics.

Refined finite-volume effect analysis.

Abstract

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account.