On the maximal cut of Feynman integrals and the solution of their differential equations

By A. Primo, L. Tancredi. 2016

171 citations recorded by the source corpus.

Abstract The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ = ( 4 − d ) / 2 , where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b6e9b0955e746839146d6c6e9feaee435f9669ba

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In Applied Mathematics

In Computational Theory and Mathematics

In Nuclear and High Energy Physics

Citations in the corpus

Ultraviolet properties of N=8 supergravity at five loops (2018, methodology): “As a cross-check for the crossed-cube topology, we have also analytically solved for the integrals in closed form by contour integration [73] using the Baikov representations [78], without making use of integral relations of the type (5.”
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].”
Cuts of Feynman Integrals in Baikov representation (2017, methodology): “Evaluating the maximally cut MI provides therefore a solution to the homogeneous equation [78, 79].”
Higgs boson production at hadron colliders at N3LO in QCD (2018, background): “[75, 76] it was demonstrated how one can find a solution for a coupled homogeneous part of a system differential equations for Feynman integrals.”
Feynman integrals and intersection theory (2018, background): “6), as was first observed in [49], and later also [39–41] in the Baikov representation.”
Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, methodology): “As it was shown in [39], given a set of master integrals, their maximal cut singles out by construction the homogeneous part of the differential equations.”
Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, methodology): “The number of MIs for a given integral family, the order of the differential equations they obey, and the classification of the homogeneous solutions according to the independent components of the integration domain, revealed a natural correspondence between the MIs and the geometric properties of t”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, background): “This continues the study from Les Houches 2015, where good agreement was shown between fixed order and parton shower Monte Carlo predictions (for non-Sudakov observables) for Higgs+jets production with one value of R (0.4).”