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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 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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Notes

  1. The Euclidean time dimension does not play any role in this review and will be always assumed to be infinite.

  2. Note that a relativistic infinite-volume amplitude [260], constructed along the same lines, was used recently [264] to address Dalitz plots of the reaction \(\tau \rightarrow \nu _\tau (a_1(1260)\rightarrow \pi \pi \pi )\).

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Acknowledgements

We thank R. Brett for a careful reading of the manuscript. The work of MD and MM is supported by the National Science Foundation under Grant no. PHY-2012289 and by the US Department of Energy under Award No. DE-SC0016582. MD is also supported by the US Department of Energy, Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177. The work of AR is funded in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 196253076—TRR 110, Volkswagenstiftung (Grant no. 93562) and the Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative (PIFI) (Grant no. 2021VMB0007).

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Mai, M., Döring, M. & Rusetsky, A. Multi-particle systems on the lattice and chiral extrapolations: a brief review. Eur. Phys. J. Spec. Top. 230, 1623–1643 (2021). https://doi.org/10.1140/epjs/s11734-021-00146-5

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