Decomposition of Feynman integrals by multivariate intersection numbers
Hjalte Frellesvig,Federico Gasparotto,Stefano Laporta,M. K. Mandal,Pierpaolo Mastrolia,Luca Mattiazzi,Sebastian Mizera +6 more
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In this paper, the authors 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.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 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.read more
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Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
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References
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Journal ArticleDOI
Integration by parts: The algorithm to calculate β-functions in 4 loops
K.G. Chetyrkin,F.V. Tkachov +1 more
TL;DR: In this paper, it was proved that the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic "algebraic" procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind.
Journal ArticleDOI
One-loop n-point gauge theory amplitudes, unitarity and collinear limits
TL;DR: In this article, the authors presented a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory, and proved that their N = 4 ansatz is correct.
Journal ArticleDOI
Fusing gauge theory tree amplitudes into loop amplitudes
TL;DR: In this paper, a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities, is identified.
Journal ArticleDOI
One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
TL;DR: In this paper, the authors presented a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory, and proved that their $N=4$ ansatz is correct using general properties of the relevant one-loops $n$-point integrals.
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Multiloop integrals in dimensional regularization made simple
TL;DR: It is argued that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and criteria for finding an optimal basis are proposed.