3-body quantization condition in a unitary formalism

TL;DR

This paper develops a relativistic 3-body quantization condition based on unitarity principles, enabling the extraction of finite-volume spectra from lattice QCD and matching with experimental data.

Contribution

It introduces a new fully relativistic 3-body quantization condition derived from unitarity constraints and applies it to the $^+^+^+$ system, aligning with lattice results.

Findings

Derived a relativistic 3-body quantization condition.

Successfully matched finite-volume spectra with lattice QCD results.

Provided a framework for analyzing 3-body systems in lattice QCD.

Abstract

Unitarity identifies all power-law finite-volume effects and is, therefore, the crucial S-matrix principle for a mapping between experimental results and those of Lattice QCD calculations. In this contribution we review how 3-body unitarity constrains the form of the 3-body scattering amplitude parametrized by the tower of isobars. The result is discretized and projected to the irreducible representations of the cubic group, leading to a fully relativistic 3-body quantization condition. The latter is used to deduce the finite-volume excited level spectrum of the $\pi^+\pi^+\pi^+$ system, which agrees nicely with the available lattice results by the NPLQCD collaboration.