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   Articles with "feynman integrals" as a keyword



Elliptic Feynman integrals and pure functions

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recommendations! 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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recommendations! Published in 2019 at "Journal of High Energy Physics"

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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recommendations! Published in 2020 at "Journal of High Energy Physics"

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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recommendations! Published in 2019 at "Journal of High Energy Physics"

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
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A first look at the function space for planar two-loop six-particle Feynman integrals

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recommendations! 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

GKZ hypergeometric systems of the four-loop vacuum Feynman integrals

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recommendations! Published in 2024 at "Journal of High Energy Physics"

DOI: 10.1007/jhep03(2025)013

Abstract: Basing on Mellin-Barnes representations and Miller’s transformation, we present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric systems, the analytical hypergeometric solutions of 4-loop vacuum Feynman… read more here.

Keywords: hypergeometric systems; loop vacuum; gkz hypergeometric; vacuum feynman ... See more keywords

Decomposition of Feynman integrals on the maximal cut by intersection numbers

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recommendations! 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

Feynman integrals, elliptic integrals and two-parameter K3 surfaces

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recommendations! Published in 2025 at "Journal of High Energy Physics"

DOI: 10.1007/jhep06(2025)250

Abstract: The three-loop banana integral with three equal masses and the conformal two-loop five-point traintrack integral in two dimensions are related to a two-parameter family of K3 surfaces. We compute the corresponding periods and the mirror… read more here.

Keywords: two parameter; integrals elliptic; integrals two; feynman integrals ... See more keywords

Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight

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recommendations! Published in 2021 at "Journal of High Energy Physics"

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

Copositive geometry of Feynman integrals

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recommendations! Published in 2025 at "Letters in Mathematical Physics"

DOI: 10.1007/s11005-025-01961-w

Abstract: Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone.… read more here.

Keywords: copositive geometry; feynman integrals; geometry feynman; geometry ... See more keywords

Efficient computation of one-loop Feynman integrals and fixed-branch integrals to high orders in ε

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recommendations! Published in 2024 at "Physical Review D"

DOI: 10.1103/physrevd.111.094028

Abstract: We propose a novel method, called the dimension-changing transformation (), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in ε. The relates one-loop Feynman integrals or fixed-branch integrals in a… read more here.

Keywords: fixed branch; feynman integrals; one loop; loop feynman ... See more keywords