Abstract The spectrum of hadrons is the manifestation of color confinement of quantum chromodynamics. Hadronic resonances correspond to poles of the S -matrix. Since 2003, lots of new hadron resonant structures were discovered in the mass regions from light mesons to hadrons containing a pair of a heavy quark and an antiquark. Many of them are candidates of exotic hadrons, and they are usually observed as peaks in invariant mass distributions. However, the S -matrix also has kinematical singularities due to the on-shellness of intermediate particles for a process, such as two-body thresholds and triangle singularities (TSs), and they can produce peaks as well. On the one hand, such singularities may be misidentified as resonances; on the other hand, they can be used as tools for precision measurements. In this paper, we review the threshold cusps and various triangle singularities in hadronic reactions, paying attention to their manifestations in phenomena related to exotic hadron candidates.

中文翻译：

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强子反应中的阈值尖峰和三角形奇点

摘要 强子的光谱是量子色动力学颜色限制的表现。强子共振对应于 S 矩阵的极点。自2003年以来，在从轻介子到包含一对重夸克和一个反夸克的强子的质量区域中发现了许多新的强子共振结构。它们中的许多是奇异强子的候选者，它们通常作为不变质量分布的峰值被观察到。然而，由于中间粒子在壳上的作用，S 矩阵也具有运动学奇点，例如二体阈值和三角形奇点 (TS)，它们也可以产生峰值。一方面，这种奇点可能被误认为是共振；另一方面，它们可以用作精密测量的工具。在本文中，