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 and uniform formula for iterative reduction of one-loop integrals
Jiaqi Chen,Bo Feng +1 more
A study of Feynman integrals with uniform transcendental weights and their symbology
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Coaction and double-copy properties of configuration-space integrals at genus zero
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Les Houches 2021 - Physics at TeV Colliders: Report on the standard model precision wishlist
TL;DR: In this article , the authors reviewed recent progress in fixed-order computations for LHC applications and discussed necessary ingredients for such calculations such as parton distribution functions, amplitudes, and subtraction methods.
References
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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.
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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.