2021/08/31 by Gudrun Heinrich, G. Heinrich, Stephan C. Jahn +14
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Algorithm #Amplitude #Applied mathematics #Artificial intelligence #Asymptotic expansion #Calculus (dental) #Computer science #Electromagnetic Scattering and Analysis #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Mechanism (biology) #Perspective (graphical) #Physics #Programming language #Theoretical computer science #Toolbox #hep-ph
paper · pdf · doi:10.1016/j.cpc.2021.108267
published as Computer Physics Communications 273 (2022) 108267 · 43 pages, 12 figures; replaced by version published in CPC
openalex publication_date 2021/12/29 · arxiv created 2022/01/26 · arxiv updated 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We discuss the technique of expansion by regions from a geometric perspective, and its implementation within py SecDec , a toolbox for the evaluation of dimensionally regulated parameter integrals. The program offers an automated way to perform asymptotic expansions and provides a new mechanism for efficiently evaluating amplitudes, as well as individual integrals. The usage of the new features available within py SecDec is illustrated with several examples. Program summary Program Title: py SecDec CPC Library link to program files: https://doi.org/10.17632/dnrkf5jxzh.3 Developer's repository link: https://github.com/gudrunhe/secdec , https://secdec.readthedocs.io (online documentation) Licensing provisions: GNU Public License v3 Programming language: Python, Form , C++, Cuda External routines/libraries: GSL [1], NumPy [2], SymPy [3], Nauty [4], Cuba [5], Form [6], GiNaC [7]; optionally Normaliz [8]. Journal reference of previous version: Comput. Phys. Commun. 240 (2019) 120–137 . Does the new version supersede the previous version?: Yes Nature of problem: Expansion of Feynman integrals in different kinematic limits, regularisation of ultraviolet, infrared and spurious singularities, numerical integration in the presence of integrable singularities (e.g. kinematic thresholds). Solution method: After specification of the desired kinematic limit by the user (definition of a smallness parameter), the regions contributing to the integral are determined and expansion in the smallness parameter up to the desired order is performed. Extraction of singularities in the dimensional regularization parameter as well as in analytic regulators for potential spurious singularities is done using sector decomposition. This leads to a Laurent series in the regularization parameters, where the coefficients are finite integrals over the unit hypercube. Integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. The integrals expanded in the different regions are summed and evaluated numerically. References [1] M. Galassi et al., GNU Scientific Library Reference Manual. ISBN:0954612078 , http://www.gnu.org/software/gsl/ . [2] C. R. Harris, K. J. Millman, S. J. van der Walt, et al., Array programming with NumPy, Nature 585 (2020) 357–362. 10.1038/s41586-020-2649-2 , http://www.numpy.org/ . [3] A. Meurer, et al., SymPy: symbolic computing in Python, PeerJ Comp. Sci. 3 (2017) e103. 10.7717/peerj-cs.103 , http://www.sympy.org/ . [4] B. D. McKay and A. Piperno, Practical graph isomorphism, II, J. Symb. Comput. 60 (2014) 94–112. 10.1016/j.jsc.2013.09.003 , http://pallini.di.uniroma1.it . [5] T. Hahn, CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78. arXiv:hep-ph/0404043 , http://www.feynarts.de/cuba/ . [6] J. Kuipers, T. Ueda and J. A. M. Vermaseren, Code Optimization in FORM, Comput. Phys. Commun. 189 (2015) 1. arXiv:1310.7007 , http://www.nikhef.nl/~form/ . [7] C. W. Bauer, A. Frink, and R. B. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2002) 1–12. arXiv:cs/0004015 , https://www.ginac.de/ . [8] W. Bruns, B. Ichim, B. and T. Römer, C. Söger, Normaliz. Algorithms for rational cones and affine monoids. http://www.math.uos.de/normaliz/ .