The diamond rule for multi-loop Feynman diagrams

Abstract

An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed.

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• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Forcer: a FORM program for 4-loop massless propagators
• The propagator seagull: general evaluation of a two loop diagram
• Calculating four-loop massless propagators with Forcer
• Recursion-free solution for two-loop vacuum integrals with "collinear" masses
• Kite diagram through Symmetries of Feynman Integrals
• Track 3: Computations in theoretical physics -- techniques and methods