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.

本文梳理了Package-X首次重大更新的新增功能与改进项。Package-X 2.0现已可生成任意高阶维正规化张量积分(dimensionally regulated tensor integrals)的解析表达式，该积分最多包含四个不同传播子(propagator)，每个传播子带有任意整数幂次，适用于任意偶数维时空附近的场景，可在（近乎）任意实值运动学点(kinematic point)处给出紫外发散(UV divergent)、红外发散(IR divergent)与有限部分结果。此外，该工具还可针对任意非奇异运动学点，将上述积分展开为任意阶的多变量泰勒级数展开(Taylor series expansion)。Package-X 2.0输出的所有特殊函数与符号缩写，均支持Mathematica的任意精度求值(arbitrary precision evaluation)能力，可有效解决数值稳定性(numerical stability)相关问题。最后，Package-X的张量代数运算例程(tensor algebraic routines)已得到优化与扩展，可支持在壳(on shell)与脱壳(off shell)的开放费米子链(fermion chain)。其配套文档（等效超100页印刷篇幅）可通过Mathematica的Wolfram文档中心(Wolfram Documentation Center)访问，涵盖Package-X所有符号的相关说明，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的对接指南。
该程序的旧版本（AEXT_v1_0）可通过以下链接获取：http://dx.doi.org/10.1016/j.cpc.2015.08.017。