Golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs

Abstract

We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis integrals numerically, using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with massless internal particles in a fast and numerically stable way. Program summaryProgram title: golem95_v1.0Catalogue identifier: AEEO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEO_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.: 50 105No. of bytes in distributed program, including test data, etc.: 241 657Distribution format: tar.gzProgramming language: Fortran95Computer: Any computer with a Fortran95 compilerOperating system: Linux, UnixRAM: RAM used per form factor is insignificant, even for a rank six six-point form factorClassification: 4.4, 11.1External routines: Perl programming language (http://www.perl.com/)Nature of problem: Evaluation of one-loop multi-leg tensor integrals occurring in the calculation of next-to-leading order corrections to scattering amplitudes in elementary particle physics.Solution method: Tensor integrals are represented in terms of form factors and a set of basic building blocks (“basis integrals”). The reduction to the basis integrals is performed numerically, thus avoiding the generation of large algebraic expressions.Restrictions: The current version contains basis integrals for massless internal particles only. Basis integrals for massive internal particles will be included in a future version.Running time: Depends on the nature of the problem. A rank 6 six-point form factor at a randomly chosen kinematic point takes 0.13 seconds on an Intel Core 2 Q9450 2.66 GHz processor, without any optimisation. With compiler optimisation flag -O3 the same point takes 0.09 seconds. Timings for lower point form factors are: All form factors for five-point functions from rank 0 to rank 4: 0.04 s. All form factors for rank 5 five-point functions: 0.05 s. All form factors for four-point functions from rank 0 to rank 4: 0.01 s.