Four-point function in general kinematics through geometrical splitting and reduction

Abstract

It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the dimensionally-regulated one-loop four-point function in general kinematics is presented.

8 pages, 9 figures, contribution for proceedings of ACAT 2017 (Seattle, USA, August 21-25, 2017). arXiv admin note: substantial text overlap with arXiv:1605.04828

References in corpus (5)

• Geometrical methods in loop calculations and the three-point function
• New relationships between Feynman integrals
• Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
• The geometry of one-loop amplitudes
• Geometrical splitting and reduction of Feynman diagrams

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• Massive Conformal Symmetry and Integrability for Feynman Integrals
• From positive geometries to a coaction on hypergeometric functions
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Functional relations for elliptic polylogarithms
• Yangian Bootstrap for Massive Feynman Integrals
• Functional reduction of one-loop Feynman integrals with arbitrary masses