FeynHelpers: Connecting FeynCalc to FIRE and Package-X

Abstract

We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides a library of analytic results for scalar 1-loop integrals with up to 4 legs, while the latter is a general-purpose tool for reduction of multi-loop scalar integrals using Integration-by-Parts (IBP) identities. Program summaryProgram Title: FeynHelpersProgram Files doi:http://dx.doi.org/10.17632/h5cfbhbbnc.1Licensing provisions: GNU Public License 3Programming language: Wolfram Mathematica 8 and higherExternal routines/libraries: FeynCalc [1,2], FeynArts [3], FeynRules [4], Package-X [5], FIRE [6]Nature of problem: FeynCalc is missing built-in capabilities to provide analytic results for scalar 1-loop integrals and to reduce multi-loop integrals using Integration-by-Parts (IBP) identities. These short-comings limit the usefulness of the package for the fully analytic evaluation of Feynman diagrams.Solution method: An easy-to-use interface implemented in Wolfram Mathematica seamlessly integrates two other Mathematica packages (Package-X and FIRE) into FeynCalc.Restrictions: The interface to FIRE currently misses the ability to recognize loop integrals that belong to the same topology, which means that each integral is processed separately. Furthermore, starting and stopping parallel kernels requires around 1.5 seconds per integral, which can be too slow, when hundreds of integrals are involved. [1]R. Mertig, M. Böhm, and A. Denner, Feyn Calc - Computer-algebraic calculation of Feynman amplitudes, Comput. Phys. Commun., 64, 345–359, (1991).[2]V. Shtabovenko, R. Mertig, and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun., 207, 432–444, (2016), arXiv:1601.01167.[3]T. Hahn, Generating Feynman Diagrams and Amplitudes with FeynArts 3, Comput. Phys. Commun., 140, 418–431, (2001), arXiv:hep-ph/0012260.[4]N. D. Christensen and C. Duhr, FeynRules - Feynman rules made easy, Comput. Phys. Commun., 180, 1614–1641, (2008), arXiv:0806.4194.[5]H. H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun., 197, 276–290, (2015), arXiv:1503.01469.[6]A. V. Smirnov and V. A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun., 184, 2820–2827, (2013), arXiv:1302.5885.