Scalar one-loop 4-point integrals

By Ansgar Denner, Stefan Dittmaier. 2010

229 citations recorded by the source corpus.

Abstract We provide a complete set of results for the scalar 4-point function appearing in one-loop calculations in QCD, QED, the electroweak Standard Model and popular extensions thereof. Complex internal masses, which are needed for calculations involving unstable particles, are supported throughout, whereas complex momenta are not supported. In particular, for the most general, regular case we present two independent results in terms of 72 and 32 dilogarithms. In addition we list explicit results for all soft- and/or collinear-singular cases in dimensional regularization, mass regularization, and in regularizations of mixed type. The exceptional case with a vanishing modified Cayley determinant, which hardly appears in applications, is not considered.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5de63a8d9dd875af06fe7c9a912ec412325afbd7

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In Nuclear and High Energy Physics

Citations in the corpus

Electroweak radiative corrections for collider physics (2019, background): “[179] for the 4-point function and of Ref.”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “[554], or with CutTools [555], which implements the OPP method [95], together with the OneLOop library [556], the employed recursion permits to achieve very high CPU performance and a high degree of numerical stability.”
Collier: A fortran-based complex one-loop library in extended regularizations (2016, background): “[59], where results for all relevant (regular and IR-singular) cases in scattering processes, both in mass and dimensional regularization, have been presented.”
NLO electroweak automation and precise predictions for W + multijet production at the LHC (2014, methodology): “To this end, OpenLoops is interfaced with the Collier library [82], which implements the Denner-Dittmaier reduction techniques [83, 84] and the scalar integrals of [85].”
Automated event generation for loop-induced processes (2015, background): “[13] suggest that it might not hold true for the private TIR implementation in COLLIER [32, 33].”
On-the-fly reduction of open loops (2017, methodology): “By default, OpenLoops 1 adopts the tensor representation on the rhs of (60) and computes the relevant tensor integrals with the Collier library [19], which implements the reduction techniques of [4,63] and the scalar integrals of [64].”
Electroweak corrections to dilepton + jet production at hadron colliders (2011, methodology): “[89] for 4point functions with complex internal masses and on the methods and results of ref.”
W±Z production at the LHC: fiducial cross sections and distributions in NNLO QCD (2016, methodology): “or 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 integrals of Ref. [49]. To guarantee numerical stability in exceptional phase-space regions | more precisely for phase”
NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders (2012, background): “[55], where explicit analytic continuations of box integrals have been presented for all kinematic configurations that are relevant for physical processes.”
Gluon-induced Higgs-strahlung at next-to-leading order QCD (2012, unknown): “[48–53].”
Mass effects in the Higgs-gluon coupling: boosted vs. off-shell production (2014, methodology): “In this paper we extend this implementation by top (and bottom) mass effects at leading order accuracy by using loop–level matrix elements provided by OpenLoops [90–93], which we use for reweighting the effective theory.”