New developments in FeynCalc 9.0

Abstract

Abstract In this note we report on the new version of FeynCalc , a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory. The main features of version 9.0 are: improved tensor reduction and partial fractioning of loop integrals, new functions for using FeynCalc together with tools for reduction of scalar loop integrals using integration-by-parts (IBP) identities, better interface to FeynArts and support for S U ( N ) generators with explicit fundamental indices. Program summary Program title: FeynCalc Catalogue identifier: AFBB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFBB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Public Licence 3 No. of lines in distributed program, including test data, etc.: 734115 No. of bytes in distributed program, including test data, etc.: 6890074 Distribution format: tar.gz Programming language: Wolfram Mathematica 8 and higher. Computer: Any computer that can run Mathematica 8 and higher. Operating system: Windows, Linux, OS X. Classification: 4.4, 5, 11.1. External routines: FeynArts [2] (Included) Nature of problem: Symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory. Solution method: Algebraic identities that are needed for evaluation of Feynman Reasons for new version: Compatibility with Mathematica 10, improved performance and new features regarding manipulation of loop integrals. Restrictions: Slow performance for multi-particle processes (beyond 1 → 2 and 2 → 2 ) and processes that involve large ( > 100) number of Feynman diagrams. Additional comments: The original FeynCalc paper was published in Comput. Phys. Commun., 64 (1991) 345, but the code was not included in the Library at that time. Reasons for the new version: Compatibility with Mathematica 10, improved performance and new features regarding manipulation of loop integrals. Summary of revisions: Tensor reduction of 1-loop integrals is extended to arbitrary rank and multiplicity with proper handling of integrals with zero Gram determinants. Tensor reduction of multi-loop integrals is now also available (except for cases with zero Gram determinants). Partial fractioning algorithm of [1] is added to decompose loop integrals into terms with linearly independent propagators. Feynman diagrams generated by FeynArts can be directly converted into FeynCalc input for subsequent evaluation. Running time: Depends on the complexity of the calculation. Seconds for few simple tree level and 1-loop Feynman diagrams; Minutes or more for complicated diagrams. References: [1] F. Feng, $Apart: A Generalized Mathematica Apart Function, Comput. Phys. Commun., 183, 2158–2164, (2012), arXiv:1204.2314 . [2] T. Hahn, Generating Feynman Diagrams and Amplitudes with FeynArts 3, Comput. Phys. Commun., 140, 418–431, (2001), arXiv:hep-ph/0012260 .