FIRE5: A C++ implementation of Feynman Integral REduction

Abstract

In this paper the C++ version of FIRE is presented — a powerful program performing Feynman integral reduction to master integrals. All previous versions used only Wolfram Mathematica, the current version mostly uses Wolfram Mathematica as a front-end. However, the most complicated part, the reduction itself can now be done by C++, which significantly improves the performance and allows one to reduce Feynman integrals in previously impossible situations. Program summaryProgram title: FIRE5Catalogue identifier: AEPW_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPW_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 2No. of lines in distributed program, including test data, etc.: 681856No. of bytes in distributed program, including test data, etc.: 40047357Distribution format: tar.gzProgramming language: Wolfram Mathematica 6.0 or higher, C++.Computer: Starting from a desktop PC.Operating system: Linux 64bit, Mac OS X 10.6 or higher 64bit.Has the code been vectorized or parallelized?: YesRAM: Depends on the complexity of the problemClassification: 4.4, 4.8, 5, 20.External routines: Wolfram Mathematica [1], Snappy [2], KyotoCabinet [3], Fermat [4], LiteRed [5].Does the new version supersede the previous version?: YesNature of problem:Reducing Feynman integrals to master integrals can be treated as a task to solve a huge system of sparse linear equations with polynomial coefficients.Solution method:Since the matrix of equations is very specific, none of the standard methods of solving linear equations can be applied efficiently. The program approaches solving those equations with a special version of Gauss elimination. The data preparation and result analysis is performed in Wolfram Mathematica [1], but the main reduction procedure is written in C++; FIRE compresses data with the use of the Snappy [2] library, stores it on disk with the use of the KyotoCabinet [3] database engine, and performs algebraic simplifications with the Fermat [4] program. The external package LiteRed [5] can be used to produce additional rules for reduction.Reasons for new version:The Mathematica version of FIRE is too slow to perform reduction where it is needed in the current state of Elementary Particle Physics. Hence the most time-consuming part of FIRE was rewritten in C++.Summary of revisions:FIRE5 is a major update of FIRE4 — the reduction was completely rewritten (now in C++ instead of Wolfram Mathematica), gaining a huge speed advantage. Apart from that, FIRE is made backward-compatible with the previous versions.Restrictions:The complexity of the problem is mostly restricted by CPU time required to perform the reduction of integrals and the available RAM. The program has the following limits: maximal number of indices=21, maximal number of positive indices=15, maximal number of non-trivial sectors=128×256−3=32765 (global symmetries decrease the number of sectors, indices that cannot be positive do not double the number of sectors).Additional comments:Additional information may be found at http://science.sander.su.Running time:Depends on the complexity of the problem.