SecDec: A general program for sector decomposition
We present a program for the numerical evaluation of multi-dimensional polynomial parameter integrals. Singularities regulated by dimensional regularisation are extracted using iterated sector decomposition. The program evaluates the coefficients of a Laurent series in the regularisation parameter. It can be applied to multi-loop integrals in Euclidean space as well as other parametric integrals, e.g. phase space integrals. Program summary Program title: SecDec Catalogue identifier: AEIR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 57617 No. of bytes in distributed program, including test data, etc.: 895 550 Distribution format: tar.gz Programming language: Wolfram Mathematica, perl, Fortran Computer: From a single PC to a cluster, depending on the problem Operating system: Unix, Linux RAM: Depends on the complexity of the problem Classification: 4.4, 5, 11.1 Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories, e.g. multi-loop Feynman integrals, Wilson loops, phase space integrals. Solution method: Algebraic extraction of singularities in dimensional regularisation using iterated sector decomposition. This leads to a Laurent series in the dimensional regularisation parameter epsilon, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration. Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. Multi-scale integrals can only be evaluated at Euclidean points. Running time: Between a few minutes and several days, depending on the complexity of the problem. (C) 2011 Elsevier B.V. All rights reserved.
infrared singularities perturbation theory feynman diagrams multi-dimensional parameter integrals numerical integration