AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow

• Published in: Computer physics communications Vol. 283; p. 108565
• Main Authors: Liu, Xiao, Ma, Yan-Qing
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-2023
• Subjects: Differential equations; Feynman integrals; Numerical evaluation; Feynman integrals; Numerical evaluation; Differential equations
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2022.108565

AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter and their results can be obtained by constructing and solving linear differential systems with respect to this parameter, in an automatic way. The usage of this package is described in detail through an explicit example of double-box family involved in two-loop tt¯ hadroproduction.
Program title:AMFlow
CPC Library link to program files:https://doi.org/10.17632/nrkrw83bw5.1
Developer's repository link:https://gitlab.com/multiloop-pku/amflow
Licensing provisions: MIT
Programming language:Wolfram Mathematica 11.3 or higher
External routines:Wolfram Mathematica [1], FiniteFlow [2], LiteRed [3], Kira [4], FIRE [5]
Nature of problem: Automatically obtaining high-precision numerical results for dimensionally regularized Feynman integrals at arbitrary points in phase-space.
Solution method: The program implements recently proposed auxiliary mass flow method, which introduces an auxiliary mass parameter to Feynman integrals and solves differential equations with respect to this parameter to obtain physical results.
[1]http://www.wolfram.com/mathematica, commercial algebraic software.[2]https://github.com/peraro/finiteflow, open source.[3]http://www.inp.nsk.su/~lee/programs/LiteRed, open source.[4]https://gitlab.com/kira-pyred/kira, open source.[5]https://bitbucket.org/feynmanIntegrals/fire, open source.