Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP02(2019)139
Keywords
Scattering Amplitudes; Differential and Algebraic Geometry
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Funding
- Perimeter Institute for Theoretical Physics
- Supporting TAlent in ReSearch at Padova University (UniPD STARS Grant 2017)
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Research, Innovation and Science
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We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts in arbitrary space-time dimension. We introduce a minimal basis of differential forms with logarithmic singularities on the boundaries of the corresponding integration cycles. We give an algorithm for computing a basis decomposition of an arbitrary maximal cut using so-called intersection numbers and describe two alternative ways of computing them. Furthermore, we show how to obtain Pfaffian systems of differential equations for the basis integrals using the same technique. All the steps are illustrated on the example of a two-loop non-planar triangle diagram with a massive loop.
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