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A practical criterion of irreducibility of multi--loop Feynman integrals

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arxiv hep-ph/0507053 v2 pith:6MBS46OR submitted 2005-07-05 hep-ph

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

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A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 75 citations worldwide. Full citation record

  1. The two-loop fully differential soft function for $Q\bar{Q}V$ production at lepton colliders

    hep-ph 2024-11 accept novelty 8.0 of 10

    The two-loop soft function fully differential in the total momentum of real radiation in QQV production is computed analytically in terms of Goncharov polylogarithms.

  2. Landau's Leviathans

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.

  3. Tame multi-leg Feynman integrals beyond one loop

    hep-ph 2024-12 reject novelty 7.0 of 10

    A 'branch' reformulation of Feynman integrals claims to reduce multi-loop integrals to one-loop-like low-dimensional integrals, but the advertised parameter bound is wrong and the numerical validation is not shown.

  4. On the spanning cuts consistency problem in the IBP reductions of Feynman integrals

    hep-ph 2026-06 unverdicted novelty 6.0 of 10

    Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between p...

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