Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 supports Mathematica’s arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica’s Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools. The previous version of this program (AEXT_v1_0) may be found at http://dx.doi.org/10.1016/j.cpc.2015.08.017.

本文综述了Package-X首个重大更新版本的新增功能与改进之处。Package-X 2.0现已可生成任意高阶维数正规化张量积分的解析表达式，该类积分最多包含四个不同传播子，每个传播子带有任意整数权重，且可针对任意偶数时空维度进行计算，能够在（几乎）任意实值运动学点处给出紫外发散（UV divergent）、红外发散（IR divergent）与有限部分结果。此外，该软件包还可针对上述积分，在任意非奇异运动学点处生成任意阶的多变量泰勒级数展开式。Package-X 2.0输出的所有特殊函数与缩写均支持Mathematica的任意精度计算功能，以解决数值稳定性相关问题。最后，Package-X的张量代数运算模块已得到优化与扩展，可支持在壳与离壳情况下的开放费米子链运算。其配套文档（等效于逾百页印刷内容）可通过Mathematica的Wolfram文档中心访问，涵盖了Package-X所有符号的相关信息，包含超过300个基础使用示例、3个项目级教程，以及与FeynCalc和LoopTools对接的操作指南。该程序的旧版本（AEXT_v1_0）可在http://dx.doi.org/10.1016/j.cpc.2015.08.017处获取。

搜集汇总

背景与挑战

背景概述

Package-X 2.0是一个Mathematica软件包，专注于单圈积分的解析计算，支持高秩张量积分、多变量泰勒级数展开和任意精度评估，适用于粒子物理等领域的研究。该数据集包含软件包文件、详细文档和教程，并兼容FeynCalc和LoopTools等工具，发布于2017年，采用CC BY 4.0许可证。