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

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arxiv 2007.00507 v2 pith:7QYYSKGT submitted 2020-07-01 hep-ph

classification hep-ph
keywords integralscutsconstructingfeynmanfunctionsmethodparametricrepresentation
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

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    The conservative black-hole scattering angle at fifth post-Minkowskian and second self-force order is computed in terms of K3 periods, but contains a coefficient fixed only by an ad hoc 'γ-3' prescription.

  3. Positive Integrands from Feynman Integrals in the Minkowski Regime

    hep-ph 2025-06 conditional novelty 7.0 of 10

    A method for converting Minkowski-regime Feynman parameter integrals into sums of real, positive integrands with complex prefactors, eliminating contour deformation and speeding up numerical evaluation.

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