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.

从晶格 QCD 的有限体积能级中提取二体和三体强子散射振幅和低位强子共振的特性代表了一个快速发展的研究领域。Lüscher 有限体积方法的各种修改的使用为计算晶格上的无限体积散射幅度开辟了道路。最近针对不同的二体和三体散射过程获得了许多新结果，包括从晶格数据中提取共振极及其特性。然而，此类研究需要对无限体积散射幅度进行稳健的参数化，这依赖于S 的基本属性-矩阵理论，并且——最好是——包含在物理点和远离物理点的夸克质量的系统。本综述讨论了由单一化手性扰动理论提供的此类参数化。由于对该领域的兴趣迅速增长，因此特别关注晶格上的三体系统。在这里，我们简要调查了晶格数据的形式化、手性外推以及有限体积分析。