Graphic method for arbitrary n-body phase space

• 作者: Hao-Jie Jing Chao-Wei Shen Feng-Kun Guo
• 来源期刊: 科学通报（英文版）
• 年，卷（期）: 2021,（7）
• 所属期刊栏目: SHORT COMMUNICATIONS
• 页码范围: 653-656
• 页数: 4页
• 语种: 英文

摘要

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 [1].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.