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Baikov-Lee representations of cut Feynman integrals. (English) Zbl 1380.81132
Summary: 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.

MSC:
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81U05 \(2\)-body potential quantum scattering theory
81V05 Strong interaction, including quantum chromodynamics
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