Decomposition of Feynman integrals by multivariate intersection numbers

Decomposition of Feynman integrals by multivariate intersection numbers

Blog Article

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 tenga flip orb 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, sophie allport zebra 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.