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

TL;DR

This paper introduces a systematic parametric method for reducing Feynman integrals with phase space cuts using IBP identities, enabling their evaluation via differential equations.

Contribution

It develops a direct parametrization of theta functions and constructs IBP identities for integrals with cuts, advancing reduction techniques in Feynman integral calculations.

Findings

Systematic reduction of integrals with cuts using parametric IBP identities.

Facilitates evaluation of cut integrals through differential equations.

Provides a new framework for handling phase space cuts in Feynman integrals.

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.