Graphic method for arbitrary n-body phase space  

计算任意n体相空间的图形法

作　　者：Hao-Jie Jing Chao-Wei Shen Feng-Kun Guo 景豪杰;沈超玮;郭奉坤(CAS Key Laboratory of Theoretical Physics.Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China;School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China [2]School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science Bulletin》2021年第7期653-656,M0003,共5页科学通报（英文版）

基　　金：supported in part by the National Natural Science Foundation of China(11835015,11947302,11961141012;11621131001(the Sino-German Collaborative Research Center CRC110"Symmetries and the Emergence of Structure in QCD"));the Chinese Academy of Sciences(XDB34030303and QYZDB-SSW-SYS013);the CAS Center for Excellence in Particle Physics(CCEPP)。

摘　　要：In high energy physics.decay widths and cross sections areamong the most important physical observables.and the computa-tion of each of them contains a phase space integration.Therefore,the phase space integration is essential to connect theoretical cal-culations with experimental observations.It also enters into thecalculation of the imaginary part of a physical amplitude throughunitarity.Usually.in experiments.it is important for understand-ing the structure of particle spectrum whether there is a nontrivialstructure in the invariant mass distribution.在量子场论中,衰变宽度和散射截面是两个重要的物理可观测量,两者的理论计算中都包含一个相空间积分.因此,相空间积分对于连接理论计算和实验观测是非常重要的.另外,考虑S矩阵的幺正性,相空间积分还被用于物理振幅虚部的计算.实验上,末态不变质量分布上的非平庸结构(包括峰、谷以及不光滑行为等)是理解粒子谱结构的关键.因此,对于n体相空间的计算,一个核心问题是如何把部分积分变量替换为任意给定的不变质量.本文提出了一种图形法,通过若干简明的拓扑规则和对应规则,可以快速直观地得到任意参考系下任意给定不变质量的相空间公式,这将大大简化了相空间的计算,就像费曼图对振幅计算的简化一样.同时,考虑到图形法的几何本质,不局限于四维时空,对于任意维时空上的相空间计算都适用.因此,在考虑维数正规化或任意维度上的量子场论时,图形法同样可以应用于相空间的计算.

关 键 词：图形法 相空间 四维时空 变量替换 散射截面 量子场论 衰变宽度 费曼图 

分 类 号：O413.3[理学—理论物理]