Reduction of Feynman Integrals in the Parametric Representation III: Integrals with Cuts

Abstract

Phase space cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. By directly parametrizing theta functions and constructing integration-by-parts (IBP) identities in the parametric representation, we provide a systematic method to reduce integrals with cuts. Since the IBP method is available, it becomes possible to evaluate integrals with cuts by constructing and solving differential equations.

arXiv comment6 pages, 1 figure, matches published version

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• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
• Unregulated Divergences of Feynman Integrals