Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered $X$, $Y$ and $Z$ resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. Here we review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. We show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved.

中文翻译：

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晶格 QCD 和三粒子共振衰减

大多数强相互作用共振都有涉及三个或更多粒子的衰减通道，包括许多最近发现的 $X$、$Y$ 和 $Z$ 共振。为了使用晶格 QCD 从第一原理研究这种共振，必须了解计算中使用的立方体中三个粒子的有限体积效应。在这里，我们回顾了开发三粒子量化条件的努力，该条件将有限体积能量与无限体积散射幅度相关联。我们详细描述了所遵循的三种方法，并就相应结果之间的关系提出了新的结果。我们展示了所有三种方法的数值实现示例，并指出了仍有待解决的重要问题。