AMBRE—a Mathematica package for the construction of Mellin–Barnes representations for Feynman integrals

The Mathematica toolkit AMBRE derives Mellin–Barnes (MB) representations for Feynman integrals in d=4−2εd=4−2ε dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. The package uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in ε. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops.Program summaryProgram title:AMBRECatalogue identifier:ADZR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZR_v1_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:21 387No. of bytes in distributed program, including test data, etc.:100 004Distribution format:tar.gzProgramming language:MATHEMATICA v.5.0 and later versionsComputer:allOperating system:allRAM:sufficient for a typical installation of MATHEMATICAClassification:5; 11.1External routines:The examples in the package use:–MB.m [M. Czakon, Comput. Phys. Commun. 175 (2006) 559 (CPC Cat. Id. ADYG)], for expansions in ε;–CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78 (CPC Cat. Id. ADVH)], for numerical evaluation of multidimensional integrals;–CERNlib [CERN Program Library, http://cernlib.web.cern.ch/cernlib/], for the implementation of Γ and Ψ functions in Fortran.Nature of problem:Derivation of a representation for a Feynman diagram with L loops and N internal lines in d   dimensions by Mellin–Barnes integrals; the subsequent evaluation, after an analytical continuation in ε=(4−d)/2ε=(4−d)/2, has to be done with other packages.Solution method:Introduction of N   Feynman parameters xixi, integration over the loop momenta, and subsequent integration over x, introducing thereby representations of sums of monomials in x by Mellin–Barnes integrals.Restrictions:Limited by the size of the available storage space.Running time:Depending on the problem; usually seconds.