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Frellesvig, Hjalte; Gasparotto, Federico; Laporta, Stefano; Mandal, Manoj K.; Mastrolia, Pierpaolo; Mattiazzi, Luca; Mizera, Sebastian
The journal of high energy physics, 03/2021, Letnik: 2021, Številka: 3Journal Article
A bstract 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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JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
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