We present pySecDec, a new version of the program SecDec, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the ...finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.
Program Title: pySecDec
Program Files doi:http://dx.doi.org/10.17632/3y8bbz9c9v.1
Licensing provisions: GNU Public License v3
Programming language: python, FORM, C++
External routines/libraries: catch 1, gsl 2, numpy 3, sympy 4, Nauty 5, Cuba 6, FORM 7, Normaliz 8. The program can also be used in a mode which does not require Normaliz.
Journal reference of previous version: Comput. Phys. Commun. 196 (2015) 470–491.
Nature of the problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in quantum field theory. 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 ϵ (and optionally other regulators), 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. The parameter integrals forming the coefficients of the Laurent series in the regulator(s) are provided in the form of libraries which can be linked to the calculation of (multi-) loop amplitudes.
Restrictions: Depending on the complexity of the problem, limited by memory and CPU time.
References:1 https://github.com/philsquared/Catch/.2 http://www.gnu.org/software/gsl/.3 http://www.numpy.org/.4 http://www.sympy.org/.5 http://pallini.di.uniroma1.it/.6 T. Hahn, “CUBA: A Library for multidimensional numerical integration,” Comput. Phys. Commun. 168 (2005) 78 hep-ph/0404043, http://www.feynarts.de/cuba/.7 J. Kuipers, T. Ueda and J. A. M. Vermaseren, “Code Optimization in FORM,” Comput. Phys. Commun. 189 (2015) 1 arXiv:1310.7007, http://www.nikhef.nl/ form/.8 W. Bruns, B. Ichim, B. and T. Römer, C. Söger, “Normaliz. Algorithms for rational cones and affine monoids.” http://www.math.uos.de/normaliz/.
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 title: SecDec 3.0
Catalogue identifier: AEIR_v3_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v3_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.: 123828
No. of bytes in distributed program, including test data, etc.: 1651026
Distribution format: tar.gz
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
Classification: 4.4, 5, 11.1.
Catalogue identifier of previous version: AEIR_v2_1
Journal reference of previous version: Comput. Phys. Comm. 184(2013)2552
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.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.
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient ...accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.
Program Title: pySecDec, qmc
Program Files doi:http://dx.doi.org/10.17632/dnrkf5jxzh.2
Licensing provisions: GNU General Public License v3
Programming language: python, FORM, C++, CUDA
External routines/libraries: catch 1, gsl 2, numpy 3, sympy 4, Nauty 5, Cuba 6, FORM 7, Normaliz 8. The program can also be used in a mode which does not require Normaliz.
Journal reference of previous version: Comput. Phys. Commun. 222 (2018) 313–326.
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 quantum field theory. 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 ϵ (and optionally other regulators), 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. The parameter integrals forming the coefficients of the Laurent series in the regulator(s) are provided in the form of libraries which can be linked to the calculation of (multi-) loop amplitudes.
Restrictions: Depending on the complexity of the problem, limited by memory and CPU/GPU time.
References:
1 https://github.com/philsquared/Catch/.
2 http://www.gnu.org/software/gsl/.
3 http://www.numpy.org/.
4 http://www.sympy.org/.
5 http://pallini.di.uniroma1.it/.
6 T. Hahn, “CUBA: A Library for multidimensional numerical integration,” Comput. Phys. Commun. 168 (2005) 78 hep-ph/0404043, http://www.feynarts.de/cuba/.
7 J. Kuipers, T. Ueda and J. A. M. Vermaseren, “Code Optimization in FORM,” Comput. Phys. Commun. 189 (2015) 1 arXiv:1310.7007, http://www.nikhef.nl/ form/.
8 W. Bruns, B. Ichim, B. and T. Römer, C. Söger, “Normaliz. Algorithms for rational cones and affine monoids.” http://www.math.uos.de/normaliz/.
We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken ...into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.
A
bstract
We study the effects of the exact top quark mass-dependent two-loop corrections to Higgs boson pair production by gluon fusion at the LHC and at a 100 TeV hadron collider. We perform a ...detailed comparison of the full next-to-leading order result to various approximations at the level of differential distributions and also analyse non-standard Higgs self-coupling scenarios. We find that the different next-to-leading order approximations differ from the full result by up to 50 percent in relevant differential distributions. This clearly stresses the importance of the full NLO result.
We present an update of the Binoth Les Houches Accord (BLHA) to standardise the interface between Monte Carlo programs and codes providing one-loop matrix elements.
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to ...two-loop integrals involving several mass scales.
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