AI 中文总结
该研究提出Mathematica软件包FlaSR，可自动生成高阶振幅和振幅平方SU(2)味求和规则，着重U自旋，能生成振幅求和规则的完整集合，用示例说明其适用范围。
AI 中文摘要
我们提出了FlaSR，一个用于自动生成高阶振幅和振幅平方SU(2)味求和规则的Mathematica软件包，特别着重于U自旋。该软件包基于对味求和规则数学结构的最新见解。给定一个由初态和末态的粒子多重态列表定义的、与对称性相关的过程系统，以及对称性极限哈密顿量的变换性质，该软件包会生成完整的过程列表，并输出该系统的振幅和振幅平方求和规则。对于振幅求和规则，该软件包会生成所有阶对称性破缺下存在的完整集合；对于可直接转化为物理可观测量之间求和规则的振幅平方求和规则，当前版本的软件包不保证能生成完整集合。我们用一系列代表性示例来说明该软件包的适用范围。
英文摘要
We present FlaSR, a Mathematica package for the automatic generation of higher-order amplitude and amplitude-squared $SU(2)$ flavor sum rules, with a particular emphasis on $U$-spin. The package is based on recent insights into the mathematical structure of flavor sum rules. Given a system of symmetry-related processes defined by a list of particle multiplets in the initial and final states, together with the transformation properties of the symmetry-limit Hamiltonian, the package generates the full list of processes and outputs amplitude and amplitude-squared sum rules for the system. For amplitude sum rules, the package generates the complete set at all orders in symmetry breaking for which such relations exist. For amplitude-squared sum rules, which translate directly into sum rules among physical observables, the current version of the package is not guaranteed to generate the complete set. We illustrate the scope of the package with a range of representative examples.
Comments38 pages, 4 tables
