Reduction of one-loop tensor 5-point integrals

By Ansgar Denner, Stefan Dittmaier. 2002

286 citations recorded by the source corpus.

A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the occurrence of inverse Gram determinants, which potentially cause severe numerical instabilities in practical calculations. Explicit results for the 5-point tensor coefficients are presented up to rank 4. The expressions for the reduction of the relevant 1-, 2-, 3-, and 4-point tensor coefficients to scalar integrals are also included; apart from these standard integrals no other integrals are needed.

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

View Paper: https://www.semanticscholar.org/paper/6cfe4d5a5ba29b3d01a89a2b21118cfe27c15423

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In Applied Mathematics

In Computational Mathematics

In Nuclear and High Energy Physics

Citations in the corpus

Electroweak radiative corrections for collider physics (2019, methodology): “[40, 202, 203] to decompose the tensor integrals into Lorentz-covariant structures.”
NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders (2012, background): “Tensor N -point integrals with N ≥ 5 are expressed in terms of lower-rank and lowerpoint integrals exploiting the four-dimensionality of space–time [52,53].”
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties (2013, methodology): “Virtual corrections are computed with O PENLOOPS[164], an automated generator of N LO QCD amplitudes for SM processes, which uses the C OLLIER library for the numerically stable evaluation of tensor integrals [171, 172] and scalar integrals [173].”
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].”
Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, methodology): “Combined with the Collier tensor-reduction library [250], which implements the Denner–Dittmaier reduction techniques [295, 296] and the scalar integrals of Ref.”
Collier: A fortran-based complex one-loop library in extended regularizations (2016, background): “[43, 50], while the implemented results for the scalar 4-point functions can be found in Ref.”
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.”