Collier: A fortran-based complex one-loop library in extended regularizations

By Ansgar Denner, Stefan Dittmaier, Lars Hofer. Computer Physics Communications, 2016

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Abstract We present the library Collier for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. The code provides numerical results for arbitrary tensor and scalar integrals for scattering processes in general quantum field theories. For tensor integrals either the coefficients in a covariant decomposition or the tensor components themselves are provided. Collier supports complex masses, which are needed in calculations involving unstable particles. Ultraviolet and infrared singularities are treated in dimensional regularization. For soft and collinear singularities mass regularization is available as an alternative. Program summary Program title: Collier Program Files doi: http://dx.doi.org/10.17632/dmdn2ph3x2.1 Licensing provisions: GNU GPL version 3 Programming language: Fortran95 Nature of problem: Evaluation of general one-loop multi-leg scalar and tensor integrals occurring in the calculation of one-loop corrections to scattering amplitudes in relativistic quantum field theories. Solution method: Scalar integrals are evaluated using explicit analytical expressions. Tensor integrals are numerically reduced to scalar integrals via different methods. Depending on the specific kinematical variables, an appropriate method is automatically chosen to optimize the resulting numerical accuracy. Restrictions: real momenta

Subfields: Computational Theory and Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/db18efa5ff80778493f2ad9067656a184df0fea6

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Citations in the corpus

On-the-fly reduction of open loops (2017, methodology): “OPS 1 (OL1) with CUTTOOLS 1.9.5 [5] in qp, where dp-contamination inside CUTTOOLS prevents more than 16 correct digits. The scalar integrals for OL2 calculations in dp were evaluated with COLLIER 1.2 [4]. For this process, OL2 in dp yields an improvement of 1 3 orders of magnitude in numerical accur”
W±Z production at the LHC: fiducial cross sections and distributions in NNLO QCD (2016, methodology): “5], which implements a fast numerical recursion for the calculation of NLO scattering amplitudes within the SM. For the numerically stable evaluation of tensor integrals we employ the Collier library [27,28,46], which is based on the Denner{Dittmaier reduction techniques [47,48] and the scalar integ”
Higgs boson pair production at NNLO with top quark mass effects (2018, methodology): “A major element of this stability originates from the employed tensor integral reduction library COLLIER [48].”
Herwig 7.2 release note (2019, methodology): “wig plus dependencies build. herwig-bootstrap will also enforce the newest versions of external amplitude providers; specifically we now use: { OpenLoops [34] versions 2.0.0 with the Collier library [35] for tensor reduction (should older versions of OpenLoops be required, the input les require the ”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “Recola and Recola2 implement such an algorithm for computing tensor coefficients numerically for arbitrary processes in the SM and beyond, respectively, while the tensor integrals are obtained by means of the Collier library [546, 547].”
Large NLO corrections in tt¯ W ± and tt¯ tt¯ hadroproduction from supposedly subleading EW contributions (2018, methodology): “These techniques have been automated in the module MadLoop [10], which is used for the generation of the amplitudes and in turn exploits CutTools [53], Ninja [54, 55] and Collier [56], together with an in-house implementation of the OpenLoops optimisation [5].”
The automation of next-to-leading order electroweak calculations (2018, methodology): “These have been automated in the module MadLoop [17, 57], which in turn exploits CutTools [58], Ninja [59, 60], IREGI [61], or Collier [62], together with an in-house implementation of the OpenLoops optimisation [12].”
W+W− production at the LHC: fiducial cross sections and distributions in NNLO QCD (2015, methodology): “For the numerically stable evaluation of tensor integrals we employ the Collier library [27, 28, 46], which is based on the Denner-Dittmaier”
Fully differential NNLO computations with MATRIX (2017, methodology): “cluster_submit_line[1-99] Lines in cluster submit file to add cluster-specific options.”
Electroweak radiative corrections for collider physics (2019, methodology): “For tensor-integral reduction the Collier [229] library is used, while OPP reduction is performed with CutTools [239].”
Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC (2016, methodology): “nArts [58, 59] and further algebraic processing with in-house Mathematicaroutines. In all three calculational approaches, the one-loop integrals are evaluated with the tensor-integral library Collier [62] containing 8 two independent implementations of the tensor and scalar integrals. Collieremploys”