In high energy physics, decay widths and cross sections are among the most important physical observables, and the computation of each of them contains a phase space integration. Therefore, the phase space integration is essential to connect theoretical calculations with experimental observations. It also enters into the calculation of the imaginary part of a physical amplitude through unitarity. Usually, in experiments, it is important for understanding the structure of particle spectrum whether there is a nontrivial structure in the invariant mass distribution. For instance, resonances, such as excited hadrons and the Higgs particle, are often found as peaks in the invariant mass distributions of certain final state particles. Thus, a key problem of the phase space integration is to get the formula of the phase space element expressed in terms of any given invariant masses for an n-body system. When there are only two or three particles in the final state, the corresponding phase space integration is relatively easy, as given in, e.g., the chapter of Kinematics in the Review of Particle Physics citeZyla:2020zbs. When the number of final state particles is larger than 3, the phase space integration becomes much more involved. In this paper, we propose a novel method based on graphics, which can not only give the phase space formula of any given invariant masses intuitively in general D-dimensional spacetime, but also greatly simplifies the calculation just as what Feynman diagrams do in calculating scattering amplitudes.

在高能物理学中，衰变宽度和横截面是最重要的物理观测值，它们中的每一个的计算都包含相空间积分。因此，相空间积分对于将理论计算与实验观察联系起来至关重要。它还通过酉性进入物理幅度的虚部的计算。通常，在实验中，在不变的质量分布中是否存在非平凡结构对于理解粒子谱的结构很重要。例如，共振，如激发强子和希格斯粒子，通常被发现为某些最终状态粒子的不变质量分布中的峰值。因此，n-体系统。当最终状态只有两个或三个粒子时，相应的相空间积分相对容易，如 Review of Particle Physics 中的运动学章节 citeZyla:2020zbs 中给出的那样。当终态粒子数大于 3 时，相空间积分变得更加复杂。在本文中，我们提出了一种基于图形的新方法，它不仅可以在一般的D维时空中直观地给出任意给定不变质量的相空间公式，而且可以像费曼图计算散射一样大大简化计算。振幅。