$I = 3$ three-pion scattering amplitude from lattice QCD

TL;DR

This paper uses lattice QCD to analyze three-pion scattering, providing evidence for a nonzero contact interaction and comparing results with chiral perturbation theory, revealing good agreement at threshold but some discrepancies at higher energies.

Contribution

It presents the first lattice QCD analysis of the three-pion scattering amplitude with evidence for a nonzero contact term and compares findings to chiral perturbation theory.

Findings

Evidence for a nonzero contact part of the three-pion scattering amplitude.

Good agreement with chiral perturbation theory at threshold.

Tension observed in the energy-dependent part of the scattering amplitude.

Abstract

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M\approx 200\;$MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find $\sim 2 \sigma$ evidence for a nonzero value for the contact part of the three-$\pi^+$ ($I=3$) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-$\pi^+$scattering amplitude. We also find that the two-$\pi^+$ ($I=2$) spectrum is fit well by an $s$-wave phase shift that incorporates the expected Adler zero.