Abstract
Abstract In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg amplitudes. These representations are one-dimensional integrals designed to be free of instabilites induced by inverse powers of Gram determinants, therefore suitable for stable numerical implementations.
Highlights
The Golem project [1] initially aimed at automatically computing one loop corrections to QCD processes using Feynman diagrams techniques whereby 1) each diagram was written as form factors times Lorentz structures 2) each form factor was decomposed on a particular redundant set of basic integrals
The issue which we address here is the extension of this approach of one-dimensional integral representations for our set of basic integrals in the most general case, i.e. with internal complex masses
We provided a representation of one-loop, 3-point functions in 4 and 6 dimensions in the form of one dimensional representations in the general case with complex masses
Summary
The Golem project [1] initially aimed at automatically computing one loop corrections to QCD processes using Feynman diagrams techniques whereby 1) each diagram was written as form factors times Lorentz structures 2) each form factor was decomposed on a particular redundant set of basic integrals. When the form factors are reduced down to a basis of scalar integrals only, negative powers of Gram determinants, generically noted det(G) below, show up in separate coefficients of the decomposition. To handle det(G) issues, we advocate the use of one-dimensional integral representations rather than relying on Taylor expansions in powers of det(G) The latter may be thought a priori better both in terms of CPU time and accuracy, the order up to which the expansion shall be pushed may happen to be rather large. The issue which we address here is the extension of this approach of one-dimensional integral representations for our set of basic integrals in the most general case, i.e. with internal complex masses. The main body of the text presents the general arguments whereas the various technical details supporting the latter are gathered in appendices, to make the reading of this article more fluent
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