An automatized algorithm to compute infrared divergent multi-loop integrals

By Thomas Binoth, Gudrun Heinrich. 2000

497 citations recorded by the source corpus.

Abstract We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4−2ϵ dimensions, adequate subtractions lead to a Laurent series in ϵ , where the coefficients of the pole and finite terms are sums of regular parameter integrals which can be evaluated numerically. We fully automatized this algorithm by implementing it into algebraic manipulation programs and applied it to calculate numerically some nontrivial 2-loop 4-point and 3-loop 3-point Feynman diagrams. Finally, we discuss the applicability of our method to phenomenologically relevant multi-loop calculations such as the NNLO QCD corrections for e + e − → 3 jets.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/849b719f6a9466a4a8488a7a3b720f86b2723c1b

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Sector Decomposition (2008, methodology): “1 Multi-loop diagrams The first application of the algorithm presented in [16] was the numerical evaluation of massless two-loop box diagrams at certain Euclidean points(2).”
pySecDec: A toolbox for the numerical evaluation of multi-scale integrals (2017, background): “External routines/libraries: catch [1], gsl [2], numpy [3], sympy [4], Nauty [5], Cuba [6], FORM [7], Normaliz [8].”
A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions (2006, methodology): “Next, the overlapping singularities are disentangled using sector decomposition [54, 55, 56, 57, 58, 59].”
A Systematic and Efficient Method to Compute Multi-loop Master Integrals (2017, methodology): “Currently, the only method that can systematically compute any MI is the sector decomposition [30].”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “The sector decomposition algorithm [61] has seen a number of optimisations, implemented into the publicly available updates of the codes (py)SecDec [62, 63] and Fiesta [64].”
W±Z production at the LHC: fiducial cross sections and distributions in NNLO QCD (2016, methodology): “d as extensions of the NLO subtraction methods of Refs. [86{89] to NNLO. Stripper, instead, is a combination of the FKS subtraction method [86] with numerical techniques based on sector decomposition [90,91]. The methods in the second category start from an NLO calculation with one additional parton”