Package-X: A Mathematica package for the analytic calculation of one-loop integrals
Package-X: A Mathematica package for the analytic calculation of one-loop integrals
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DOI：
10.1016/j.cpc.2015.08.017
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发表时间：
2015-03
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影响因子：
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通讯作者：
Hiren H. Patel
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文献类型：
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作者：
Hiren H. Patel
本文介绍了一个用于解析计算四维时空附近维数可调的单圈积分的数学软件包Package-X. Package-X可计算任意高阶张量积分，最多可计算三个传播子，并给出了包含实值外不变量和内质量的任意运动学组态的UV发散、IR发散和有限部分的紧致表达式.输出表达式可以很容易地进行数值计算，并使用内置的Mathematicfunctions进行符号操作。重点是评价速度、结果的可读性，特别是方便用户。还包括一个例行程序来计算狄拉克矩阵的产品的痕迹，并收集投影仪，以方便计算费米子的形状因子在一个循环。程序摘要程序标题：Package-X目录标识符：AEXT_v1_0程序摘要URL：http://cpc.cs.qub.ac.uk/summaries/AEXT_v1_0.htmlProgram可从：CPC程序图书馆，皇后大学，贝尔法斯特，N。爱尔兰许可证条款：标准CPC许可证，http://cpc.cs.qub.ac.uk/licence/licence.htmlNo。分布式程序中的行，包括测试数据等：63912号分布式程序的字节数，包括测试数据等：1224562分发格式：tar. gz编程语言：Mathematica（Wolfram语言）.计算机：任何，支持Mathematica.操作系统：Windows，Mac OS X，Linux（或任何支持Mathematica 8.0或更高版本的系统）。RAM：10 MB，取决于计算大小分类：4.4，11.1。问题性质：相对论量子场论中任意高阶张量积分以及实值外部不变量和内部质量的任何运动学配置的单圈积分的解析计算。解决方法：Passarino-Veltman约化公式，Denner-Dittmaier约化公式，以及手稿中描述的两种新约化算法。限制：单圈积分仅限于涉及不超过三个传播因子的积分。不寻常的功能：包括张量代数运算和在Dirac伽玛矩阵上执行跟踪的基本例程。运行时间：对于通常在实际计算中出现的积分为5 ms到10 s;对于更高秩的张量积分则更长。
Package-X, aMathematicapackage for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described.Package-Xcomputes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-inMathematicafunctions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool.Program summaryProgram title:Package-XCatalogue identifier:AEXT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXT_v1_0.htmlProgram obtainable from:CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:63912No. of bytes in distributed program, including test data, etc.:1224562Distribution format:tar.gzProgramming language:Mathematica (Wolfram Language).Computer:Any, which supports Mathematica.Operating system:Windows, Mac OS X, Linux (or any system supporting Mathematica 8.0 or higher).RAM:10 MB, depending on size of computationClassification:4.4, 11.1.Nature of problem:Analytic calculation of one-loop integrals in relativistic quantum field theory for arbitrarily high-rank tensor integrals and any kinematic configuration of real-valued external invariants and internal masses.Solution method:Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and two new reduction algorithms described in the manuscript.Restrictions:One-loop integrals are limited to those involving no more than three propagator factors.Unusual features:Includes rudimentary routines for tensor algebraic operations and for performing traces over Dirac gamma matrices.Running time:5 ms to 10 s for integrals typically occurring in practical computations; longer for higher rank tensor integrals.