Elliptic Feynman integrals and pure functions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep01(2019)023
Abstract: A bstractWe propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-loop Feynman integrals with… read more here.
Keywords: feynman integrals; elliptic feynman; pure functions; integrals pure ... See more keywords
All orders structure and efficient computation of linearly reducible elliptic Feynman integrals
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DOI: 10.1007/jhep01(2019)169
Abstract: A bstractWe define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand,… read more here.
Keywords: linearly reducible; reducible elliptic; feynman integrals; feynman ... See more keywords
Sequential discontinuities of Feynman integrals and the monodromy group
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DOI: 10.1007/jhep01(2021)205
Abstract: We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at… read more here.
Keywords: discontinuities feynman; sequential discontinuities; integrals monodromy; feynman integrals ... See more keywords
Functional reduction of Feynman integrals
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DOI: 10.1007/jhep02(2019)173
Abstract: A bstractA method for reducing Feynman integrals, depending on several kinematic variables and masses, to a combination of integrals with fewer variables is proposed. The method is based on iterative application of functional equations proposed… read more here.
Keywords: three variables; reduction feynman; kinematic variables; feynman integrals ... See more keywords
A first look at the function space for planar two-loop six-particle Feynman integrals
Sign Up to like & getrecommendations! Published in 2022 at "Journal of High Energy Physics"
DOI: 10.1007/jhep03(2022)056
Abstract: Abstract Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we… read more here.
Keywords: loop six; planar two; feynman integrals; two loop ... See more keywords
Decomposition of Feynman integrals on the maximal cut by intersection numbers
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep05(2019)153
Abstract: A bstractWe elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method… read more here.
Keywords: intersection numbers; feynman integrals; decomposition feynman; integrals maximal ... See more keywords
Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
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DOI: 10.1007/jhep07(2021)227
Abstract: Abstract We provide a leading singularity analysis protocol in Baikov representation, for the searching of Feynman integrals with uniform transcendental (UT) weight. This approach is powered by the recent developments in rationalizing square roots and… read more here.
Keywords: feynman integrals; integrals uniform; uniform transcendental; baikov representation ... See more keywords
Determining arbitrary Feynman integrals by vacuum integrals
Sign Up to like & getrecommendations! Published in 2019 at "Physical Review D"
DOI: 10.1103/physrevd.99.071501
Abstract: By introducing an auxiliary parameter, we find a series representation for Feynman integral, which is defined as analytical continuation of a calculable series. To obtain the series representation, one only needs to deal with some… read more here.
Keywords: feynman integrals; series representation; series; vacuum integrals ... See more keywords
Cluster Algebras for Feynman Integrals.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review letters"
DOI: 10.1103/physrevlett.126.091603
Abstract: We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a C_{2} cluster algebra, and we find cluster… read more here.
Keywords: algebras feynman; feynman integrals; cluster algebras; particle ... See more keywords
Determining Feynman Integrals with Only Input from Linear Algebra.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review letters"
DOI: 10.1103/physrevlett.129.222001
Abstract: We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples… read more here.
Keywords: input linear; determining feynman; feynman integrals; integrals input ... See more keywords
Co-Homology of Differential Forms and Feynman Diagrams
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DOI: 10.3390/universe7090328
Abstract: In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in light of recent developments. Feynman integrals enter in several perturbative methods for solving non-linear PDE, starting… read more here.
Keywords: differential forms; homology differential; forms feynman; feynman integrals ... See more keywords