Integration-by-parts reductions from unitarity cuts and algebraic geometry
By Kasper J. Larsen, Yang Zhang. 2015
214 citations recorded by the source corpus.
We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.
Subfields: Computational Theory and Mathematics, Oncology, Organic Chemistry
View Paper: https://www.semanticscholar.org/paper/437407bdb7d19579c06b2981b63dbe3c5e79c35a
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In Computational Theory and Mathematics
- Gudrun Heinrich
- Hjalte Frellesvig
- Costas G. Papadopoulos
- Pierpaolo Mastrolia
- Sebastian Mizera
- P. Maierhöfer
- Jonas Klappert
- Johann Usovitsch
In Oncology
- A. Primo
- L. Tancredi
- Fabian Lange
- Pierpaolo Mastrolia
- Sebastian Mizera
- Gudrun Heinrich
- Johann Usovitsch
- Jonas Klappert
In Organic Chemistry
- A. Primo
- L. Tancredi
- Fabian Lange
- Pierpaolo Mastrolia
- Sebastian Mizera
- Gudrun Heinrich
- Johann Usovitsch
- Jonas Klappert
Citations in the corpus
- On the maximal cut of Feynman integrals and the solution of their differential equations (2016, methodology): “More in general, this connection has been largely exploited in the so-called reverse unitarity [22] method, while a new way of solving IBPs using the information coming from the unitarity cuts has been proposed in [23].”
- Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, background): “It would be interesting to study connections to the recent applications of closelyrelated mathematical topics to Feynman integrals, such as D-module theory [62], Hopf algebras [91, 121, 122], computational algebraic geometry [21, 63], finite fields arithmetic [20], and the theory of special function”
- Collider physics at the precision frontier (2020, methodology): “It employs a Gröbner basis technique [497, 438] combined with a module intersec-”
- Cuts of Feynman Integrals in Baikov representation (2017, background): “This can be achieved by the equation, known as the syzygy equation [80, 81],”
- Feynman integrals and intersection theory (2018, methodology): “[37] K.”
- 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].”