Restrictions of Pfaffian systems for Feynman integrals

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書誌事項

公開日
2023-11-28
資源種別
journal article
権利情報
  • https://creativecommons.org/licenses/by/4.0
  • https://creativecommons.org/licenses/by/4.0
DOI
  • 10.1007/jhep11(2023)202
  • 10.48550/arxiv.2305.01585
公開者
Springer Science and Business Media LLC

説明

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic variables. We model these limits, which are often singular, via <jats:italic>restrictions</jats:italic> of <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{D} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-modules. We thereby develop two different restriction algorithms: one based on gauge transformations, and another relying on the Macaulay matrix. These algorithms output Pfaffian systems containing fewer variables and of smaller rank. We show that it is also possible to retain logarithmic corrections in the limiting variable. The algorithms are showcased in many examples involving Feynman integrals and hypergeometric functions coming from GKZ systems. This work serves as a continuation of [1].</jats:p>

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