Reduction of one-loop tensor 5-point integrals

2002/12/20 by A. Denner, S. Dittmaier · 29 citations
Mathematics · Physics and Astronomy · #Cartesian tensor #Mathematical functions and polynomials #Particle physics theoretical and experimental studies #Reduction (mathematics) #Scalar (mathematics) #Slater integrals #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor field #Trigonometric integral #hep-ph

paper · pdf · doi:10.1016/s0550-3213(03)00184-6

published as Nucl.Phys.B658:175-202,2003 · 24 pages, latex, some references added

arxiv created 2002/12/20 · openalex publication_date 2003/04/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• One-loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon
• One-loop tensor integrals in dimensional regularisation

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