Semi-automatic calculations of multi-loop Feynman amplitudes with AmpRed

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-04-07 DOI:10.1016/j.cpc.2025.109607

Wen Chen

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引用次数: 0

Abstract

We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the Feynman-parameter representation. It allows for the calculations of general parametric integrals (which may not have momentum-space correspondences). Various user-friendly tools for multi-loop calculations, such as those to construct and solve differential equations for Feynman integrals, are provided. It can also deal with tensor algebras in non-relativistic field theories. Interfaces to some packages, like QGRAF and FORM, are also provided.

Program summary

Program title: AmpRed, version 1.0

CPC Library link to program files: https://doi.org/10.17632/swnf723tdh.1

Developer's repository link: https://gitlab.com/chenwenphy/ampred

Licensing provisions: MIT license

Programming language: Wolfram Mathematica 10.0, or newer

Nature of problem: Reduce Feynman amplitudes to linear combinations of master integrals, and calculate master integrals numerically.

Solution method: Reduce Feynman amplitudes by using the methods developed in refs. [1-3], and calculate master integrals recursively by using the method developed in ref. [4].

References

[1]
W. Chen, Reduction of Feynman integrals in the parametric representation, J. High Energy Phys. 02 (2020) 115.
[2]
W. Chen, Reduction of Feynman integrals in the parametric representation II: reduction of tensor integrals, Eur. Phys. J. C 81 (2021) 244.
[3]
W. Chen, Reduction of Feynman integrals in the parametric representation III: integrals with cuts, Eur. Phys. J. C 80 (2020) 1173.
[4]
W. Chen, M.-x. Luo, T.-Z. Yang, H.X. Zhu, Soft theorem to three loops in QCD and $N = 4$ super Yang-Mills theory, J. High Energy Phys. 01 (2024) 131.

查看原文本刊更多论文

用AmpRed半自动计算多环费曼幅值

我们提出了一个Mathematica软件包AmpRed，用于高精度、高效的多环费曼幅值的半自动计算。AmpRed在费曼参数表示中实现了分部积分和微分方程的方法。它允许计算一般的参数积分（可能没有动量空间对应）。提供了各种用户友好的多回路计算工具，例如用于构建和求解费曼积分微分方程的工具。它也可以处理非相对论场论中的张量代数。还提供了一些包（如QGRAF和FORM）的接口。程序摘要程序标题：AmpRed， 1.0版本cpc库链接到程序文件：https://doi.org/10.17632/swnf723tdh.1Developer's存储库链接：https://gitlab.com/chenwenphy/ampredLicensing条款：MIT许可证编程语言：Wolfram Mathematica 10.0，或更新问题的性质：减少费曼振幅到主积分的线性组合，并计算主积分数值。解决方法：利用参考文献中提出的方法减小费曼振幅。[1-3]，并使用参考文献b[4]中开发的方法递归计算主积分。陈涛，费曼积分在参数表示中的简化，高能物理学报，02 (2020):115. b[2]。参数表示中Feynman积分的约化II：张量积分的约化，j。理论物理。[j] .中国科学d辑（2008）。参数表示中Feynman积分的约化III：带切的积分，[j]。理论物理。[j] .中国科学d辑（2020）：1173.]陈,M.-x。罗,T.-Z。杨红霞，朱红霞，QCD中三环的软定理和N=4超Yang- mills理论，高能物理学报，01(2024):131。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.