# Baikov-Lee Representations Of Cut Feynman Integrals

## TL;DR

This paper introduces a new framework using Baikov-Lee representation for evaluating cut Feynman integrals, enabling better understanding of their discontinuities and solutions beyond multiple polylogarithms.

## Contribution

It develops a general method for cut Feynman integrals using Baikov-Lee representation, applying residue calculus, and solving differential equations beyond polylogarithms.

## Key findings

- Reproduces the relation between cuts and discontinuities.
- Provides complete solutions to differential equations for Feynman integrals.
- Enables direct evaluation of complex cut Feynman integrals.

## 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.