Baikov-Lee Representations Of Cut Feynman Integrals

TL;DR

The paper develops a comprehensive Baikov-Lee framework for cut Feynman integrals, extending Cutkosky rules through sequential residue calculations and explicit domain constraints to handle both single-channel and maximally-cut cases. It makes the dependence on kinematic invariants manifest and connects cuts to discontinuities, while also leveraging maximally-cut integrals to construct complete homogeneous solution sets for differential equations beyond polylogarithms. Through detailed one- and two-loop examples, the authors validate unitarity relations and demonstrate the practicality of their approach, including loop-by-loop strategies for non-polylogarithmic, elliptic-integral cases. The work provides new analytic tools for direct cut evaluations and advances in the differential-equation method for complex Feynman integrals, with explicit applications to Higgs plus jet topologies. Overall, the cut Baikov-Lee formalism broadens the scope of analytic techniques for multi-loop calculations in collider phenomenology, especially where elliptic and higher-genus structures arise.

Abstract

We develop a general framework for the evaluation of $d$-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy's residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.