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arXiv · 2008.04823

Decomposition of Feynman Integrals by Multivariate Intersection Numbers

Hjalte Frellesvig·Federico Gasparotto·Stefano Laporta·Manoj K. Mandal·Pierpaolo Mastrolia·Luca Mattiazzi·Sebastian Mizera
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Abstract

We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.

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Hjalte Frellesvig, Federico Gasparotto, Stefano Laporta, Manoj K. Mandal, Pierpaolo Mastrolia, Luca Mattiazzi, Sebastian Mizera. 2020-08-11. Decomposition of Feynman Integrals by Multivariate Intersection Numbers. https://doi.org/10.1007/jhep03(2021)027

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