Multi-particle systems on the lattice and chiral extrapolations: a brief review

TL;DR

This review discusses recent advances in extracting hadronic scattering amplitudes and resonance properties from lattice QCD, emphasizing the use of finite-volume methods, parametrizations, and chiral extrapolations, especially for three-body systems.

Contribution

It provides a comprehensive overview of the formalism, methods, and recent results in lattice QCD studies of multi-particle systems, highlighting developments in three-body analyses and chiral extrapolations.

Findings

Successful extraction of resonance poles from lattice data

Advancements in three-body finite-volume formalism

Effective parametrizations using unitarized Chiral Perturbation Theory

Abstract

The extraction of two- and three-body hadronic scattering amplitudes and the properties of the low-lying hadronic resonances from the finite-volume energy levels in lattice QCD represents a rapidly developing field of research. The use of various modifications of the L\"uscher finite-volume method has opened a path to calculate infinite-volume scattering amplitudes on the lattice. Many new results have been obtained recently for different two- and three-body scattering processes, including the extraction of resonance poles and their properties from lattice data. Such studies, however, require robust parametrizations of the infinite-volume scattering amplitudes, which rely on basic properties of $S$-matrix theory and -- preferably -- encompass systems with quark masses at and away from the physical point. Parametrizations of this kind, provided by unitarized Chiral Perturbation Theory, are discussed in this review. Special attention is paid to three-body systems on the lattice, owing to the rapidly growing interest in the field. Here, we briefly survey the formalism, chiral extrapolation, as well as finite-volume analyses of lattice data.