SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop

Abstract

SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability. Program summaryProgram title: SecDec 3.0Catalogue identifier: AEIR_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v3_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.: 123828No. of bytes in distributed program, including test data, etc.: 1651026Distribution 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_v2_1Journal reference of previous version: Comput. Phys. Comm. 184(2013)2552Does 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 within dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter, 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:•Improved user interface.•Additional new decomposition strategies.•Usage on a cluster is much improved.•Speed-up in numerical evaluation times.•Various new features (please see below).Summary of revisions:•Implementation of two new decompositions strategies based on a geometric algorithm.•Scans over large ranges of parameters are facilitated.•Linear propagators can be treated.•Propagators with negative indices are possible.•Interface to reduction programs like Reduze, Fire, LiteRed facilitated.•Option to use numerical integrator from Mathematica.•Using CQUAD for 1-dimensional integrals to improve speed of numerical evaluations.•Option to include epsilon-dependent dummy functions.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time.Running time: Between a few seconds and several hours, depending on the complexity of the problem.