Multi-particle systems on the lattice and chiral extrapolations: a brief review
02 Mar 2021-European Physical Journal-special Topics (Springer Berlin Heidelberg)-Vol. 230, Iss: 6, pp 1623-1643
TL;DR: In this paper, a review of the literature on finite-volume analysis of lattice data is presented, focusing on three-body systems on the lattice and the properties of resonance poles and their properties.
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 Luscher 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.
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TL;DR: In this article, the relativistic finite-volume formalism based on a generic effective field theory was used to determine the parameters of the two-and three-particle K-matrices.
Abstract: We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.
30 citations
TL;DR: In this paper , the authors present the current state of the art of our understanding of the spectrum of excited strongly interacting particles and discuss methods that allow for a systematic and model-independent calculation of the hadron spectrum.
24 citations
TL;DR: In this article, the authors consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless, and derive the formalism necessary to extract two-and threeparticle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume.
Abstract: We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{K}^{+}$ and ${K}^{+}{K}^{+}{\ensuremath{\pi}}^{+}$. We derive the formalism necessary to extract two- and three-particle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume. We use a relativistic formalism based on an all-orders diagrammatic analysis in generic effective field theory, adopting the methodology used recently to study the case of three nondegenerate particles. We present both a direct derivation, and also a cross-check based on an appropriate limit and projection of the fully nondegenerate formalism. We also work out the threshold expansions for the three-particle K matrix that will be needed in practical applications, both for systems with two identical particles plus a third, and also for the fully nondegenerate theory.
18 citations
TL;DR: In this article , a relativistic invariance of the quantization condition on the lattice of the octahedral group has been shown for the three-body bound state spectrum.
Abstract: A bstract A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.
10 citations
TL;DR: In this paper , the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy are reviewed, and a systematic survey of the model dependencies is presented.
10 citations
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