Logarithmic forms and differential equations for Feynman integrals
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Publication:2188611
DOI10.1007/JHEP02(2020)099zbMATH Open1435.81078arXiv1909.04777WikidataQ106762816 ScholiaQ106762816MaRDI QIDQ2188611
Author name not available (Why is that?)
Publication date: 11 June 2020
Published in: (Search for Journal in Brave)
Abstract: We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov cite{Goncharov:1996tate} that reappeared in the context of Feynman parameter integrals in cite{Spradlin:2011wp,Arkani-Hamed:2017ahv}. The dlog representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.
Full work available at URL: https://arxiv.org/abs/1909.04777
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