Three-body unitarity versus finite-volume $\pi^+\pi^+\pi^+$ spectrum from lattice QCD

TL;DR

This paper develops a formalism for analyzing three-pion systems in finite volume from lattice QCD, enabling a deeper understanding of three-body interactions and unitarity principles in hadronic physics.

Contribution

It introduces a new formalism for three-body systems in moving frames, connecting finite-volume spectra with three-body unitarity and dynamics.

Findings

Calculated three-$^+$ spectrum consistent with lattice QCD results.

Unraveled three-body dynamics linked to the $S$-matrix unitarity.

Provided a framework for future lattice QCD studies of three-body systems.

Abstract

Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab-initio understanding of these systems. We calculate the three-$\pi^+$ spectrum unraveling the three-body dynamics that is tightly intertwined with the $S$-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.