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

• Published in: The European physical journal. ST, Special topics Vol. 230; no. 6; pp. 1623 - 1643
• Main Authors: Mai, Maxim, Döring, Michael, Rusetsky, Akaki
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2021; Springer Nature B.V; Springer
• Subjects: Amplitudes; Atomic; Chiral dynamics; Classical and Continuum Physics; Condensed Matter Physics; Energy levels; Finite volume method; Materials Science; Matrix theory; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Perturbation theory; Physics; Physics and Astronomy; Quantum chromodynamics; Resonance scattering; Review; S matrix theory; Topics in Light-Quark Physics
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-021-00146-5

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 Lüscher 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.