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[Licence| Download | New Version Template] aeir_v2_0.tar.gz(2087 Kbytes)
Manuscript Title: Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
Authors: Sophia Borowka, Jonathon Carter, Gudrun Heinrich
Program title: SecDec 2.0
Catalogue identifier: AEIR_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)396
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, Infrared and threshold singularities, Numerical integration.
PACS: 12.38.Bx, 02.60.Jh, 02.70.Wz.
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 in dimensional regularisation using iterated sector decomposition. This leads to a Laurent series in the dimensional regularisation 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 parallelisation.

Summary of revisions:
  • no restriction on the kinematics for multi-loop integrals.
  • integrand can be constructed from the topologiocal cuts of the diagram.
  • possibility of full parallelisation.
  • numerical integration of multi-loop integrals written in C++ rather than Fortran.
  • possibility to loop over ranges of parameters.

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 The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0.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.