Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0

Abstract

We present the program SecDec 2.0, which contains various new features. First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities are isolated via sector decomposition, while threshold singularities are handled by a deformation of the integration contour in the complex plane. As an application, we present numerical results for various massive two-loop four-point diagrams. SecDec 2.0 also contains new useful features for the calculation of more general parameter integrals, related for example to phase space integrals. Program summaryProgram title: SecDec 2.0Catalogue identifier: AEIR_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_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.: 156829No. of bytes in distributed program, including test data, etc.: 2137907Distribution format: tar.gzProgramming language: Wolfram Mathematica, Perl, Fortran/C++.Computer: From a single PC to a cluster, depending on the problem.Operating system: Unix, Linux.RAM: Depending on the complexity of the problemClassification: 4.4, 5, 11.1.Catalogue identifier of previous version: AEIR_v1_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)1566Does the new version supersede the previous version?: YesNature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g., kinematic thresholds).Solution method: Algebraic extraction of singularities in dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter ϵ, where the coefficients are finite integrals over the unit hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way.Reasons for new version: In the previous version the calculation of multi-scale integrals was restricted to the Euclidean region. Now multi-loop integrals with arbitrary physical kinematics can be evaluated. Another major improvement is the possibility of full parallelization.Summary of revisions:•No restriction on the kinematics for multi-loop integrals.•The integrand can be constructed from the topological cuts of the diagram.•Possibility of full parallelization.•Numerical integration of multi-loop integrals written in C++ rather than Fortran.•Possibility to loop over ranges of parameters.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0.Running time: Between a few minutes and several days, depending on the complexity of the problem. Test runs provided take only seconds.