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

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 Lüscher finite-volume method has opened a path to calculate infinitevolume 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.

Hadron Spectroscopy with Lattice QCD

“…For the mapping from two-and three-body energy eigenvalues to physical, infinite-volume amplitudes, different quantization conditions have been developed [142]. For a comprehensive survey of the literature and a detailed comparison of different methods see recent reviews [143][144][145]. Following the pioneering work of Ref.…”

Towards the finite-volume spectrum of the Roper resonance

“…These methods usually require the formulation of a so-called three-body quantization condition (for some examples, see Refs. [17][18][19][20][21][22][23][24][25][26]). A very promising approach to describe three particle scattering in a finite box is the particle-dimer framework (see [27][28][29][30][31]), which reformulates the three-body problem as a two-body problem and, therefore, significantly simplifies the three-particle dynamics.…”

Relativistic-invariant formulation of the NREFT three-particle quantization condition

“…Last but not least, a three-body analog of the Lellouch-Lüscher formula for the finite-volume matrix elements [66] has been recently derived in two different settings [67,68]. These developments are extensively covered in the latest reviews on the subject, to which the reader is referred for further details [69,70].…”