The energy-dependent $\pi^+ \pi^+ \pi^+$ scattering amplitude from QCD

TL;DR

This paper presents the first non-perturbative, energy-dependent three-pion scattering amplitude derived directly from QCD using lattice calculations and a relativistic finite-volume formalism, revealing complex analytic structures.

Contribution

It introduces a novel first-principles method to determine three-hadron scattering amplitudes from lattice QCD data, including solving integral equations for the three-body K matrix.

Findings

First non-perturbative determination of three-pion scattering amplitude from QCD.

Reveals complex analytic structure and invariant mass dependence.

Provides Dalitz-like plots of the scattering rate.

Abstract

Focusing on three-pion states with maximal isospin ($\pi^+\pi^+\pi^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.