Feynman integrals and intersection theory
By Pierpaolo Mastrolia, Sebastian Mizera. Journal of High Energy Physics, 2018
192 citations recorded by the source corpus.
A bstractWe 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/aec8599a151be9cfb13612b80c7b66c4df213427
How researchers see this paper
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In Applied Mathematics
- Gudrun Heinrich
- P. Maierhöfer
- Jonas Klappert
- Fabian Lange
- Johann Usovitsch
- Pierpaolo Mastrolia
- Sebastian Mizera
- Federico Gasparotto
In Computational Theory and Mathematics
- Gudrun Heinrich
- P. Maierhöfer
- Jonas Klappert
- Johann Usovitsch
- Fabian Lange
- Hjalte Frellesvig
- Federico Gasparotto
- M. K. Mandal
In Geometry and Topology
- Gudrun Heinrich
- Fabian Lange
- Johann Usovitsch
- Jonas Klappert
- P. Maierhöfer
- Pierpaolo Mastrolia
- Sebastian Mizera
- Federico Gasparotto
Citations in the corpus
- Collider physics at the precision frontier (2020, methodology): “The original formulation of this idea was based on the Baikov representation in combination with maximal cuts [527, 519, 520].”
- Integral reduction with Kira 2.0 and finite field methods (2020, methodology): “In the last few years, new techniques have been explored and applied to integral reduction problems, employing syzygy equations [7–12], algebraic geometry [13–15], intersection numbers [16–20], finite field and interpolation techniques [21–26], or special integral representations [27–30].”
- Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, methodology): “We provide a systematic presentation of the novel method for the decomposition of Feynman integrals onto a basis of master integrals by projections [2, 5, 6], through the intersection numbers of differential forms [3, 7], thereby avoiding the computationally expensive system-solving strategy in case”