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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NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals
TL;DR: The NeatIBP as mentioned in this paper package automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals, which can subsequently be used for either finite field reduction or analytic reduction.
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Feynman integral reduction using Gröbner bases
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Generation function for one-loop tensor reduction
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The recursive structure of Baikov representations I: generics and application to symbology
Xuhang Jiang,Li Lin Yang +1 more
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Intersection Numbers in Quantum Mechanics and Field Theory
TL;DR: In this paper , the intersection theory for twisted de Rham cohomologies is applied to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum Mechanics and Green's functions in Field Theory, and the intersection numbers for twisted cocycles can be used to derive linear and quadratic relations among them.
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.
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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.
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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.
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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.