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[Licence| Download | New Version Template] aeir_v3_0.tar.gz(1612 Kbytes)
Manuscript Title: SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
Authors: S. Borowka, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk, T. Zirke
Program title: SecDec 3.0
Catalogue identifier: AEIR_v3_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 196(2015)470
Programming 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 problem
Keywords: Perturbation theory, Feynman diagrams, multi-loop, numerical integration.
Classification: 4.4, 5, 11.1.

Does the new version supersede the previous version?: Yes

Nature 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

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.