Reduction of Feynman Integrals in the Parametric Representation IV: Integrals with Irregular Integration Regions

TL;DR

This paper presents a method to convert Feynman integrals with irregular regions into standard forms, enabling the use of existing reduction techniques, with applications to energy correlators and potential for broader event shape analyses.

Contribution

It introduces a novel approach to handle irregular integration regions in parametric Feynman integrals, expanding the applicability of reduction methods.

Findings

Irregular integrals can be transformed into standard parametric integrals.

Applied method to three-point energy correlators.

Potential to extend to various event shapes and jet observables.

Abstract

Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for which a reduction method is known. An application of this method to the analytic calculation of three-point energy correlators is presented. In principle, this method applies to more general event shapes and even jet observables.