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We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under…

High Energy Physics - Theory · Physics 2022-03-09 Johannes Broedel , Claude Duhr , Nils Matthes

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with…

High Energy Physics - Phenomenology · Physics 2018-04-04 Roman N. Lee , Alexander V. Smirnov , Vladimir A. Smirnov

We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of…

High Energy Physics - Theory · Physics 2015-06-16 Johannes M. Henn , Alexander V. Smirnov , Vladimir A. Smirnov

Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…

High Energy Physics - Phenomenology · Physics 2023-01-04 Ievgen Dubovyk , Ayres Freitas , Janusz Gluza , Krzysztof Grzanka , Martijn Hidding , Johann Usovitsch

A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…

High Energy Physics - Phenomenology · Physics 2020-03-18 Costas G. Papadopoulos , Christopher Wever

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…

High Energy Physics - Theory · Physics 2010-04-05 A. P. Isaev

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

High Energy Physics - Phenomenology · Physics 2016-04-14 Johannes Bluemlein , Khiem Hong Phan , Tord Riemann

We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularisation parameter $\varepsilon$. This is done by transforming the…

High Energy Physics - Phenomenology · Physics 2018-10-10 Luise Adams , Ekta Chaubey , Stefan Weinzierl

We 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, which we…

High Energy Physics - Phenomenology · Physics 2019-01-17 Martijn Hidding , Francesco Moriello

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

We investigate $\varepsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms.…

High Energy Physics - Theory · Physics 2024-06-12 Hjalte Frellesvig , Stefan Weinzierl

We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…

High Energy Physics - Phenomenology · Physics 2007-05-23 A. B. Arbuzov , A. V. Belitsky , E. A. Kuraev , B. G. Shaikhatdenov

We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two…

High Energy Physics - Theory · Physics 2024-11-07 Samuel Abreu , Dmitry Chicherin , Vasily Sotnikov , Simone Zoia

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…

High Energy Physics - Phenomenology · Physics 2021-10-13 Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…

High Energy Physics - Phenomenology · Physics 2025-11-21 Tommaso Armadillo

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…

High Energy Physics - Phenomenology · Physics 2026-04-03 Yuanche Liu , Antonela Matijašić , Tiziano Peraro , Yingxuan Xu , Zihua Yang , Yang Zhang

An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…

High Energy Physics - Phenomenology · Physics 2022-11-15 G. Dallabona , O. A. Battistel

In this talk we show that dual conformal symmetry has unexpected applications to Feynman integrals in dimensional regularization. Outside $4$ dimensions, the symmetry is anomalous, but still preserves the unitarity cut surfaces. This…

High Energy Physics - Theory · Physics 2018-07-24 Zvi Bern , Michael Enciso , Harald Ita , Mao Zeng

We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…

High Energy Physics - Phenomenology · Physics 2022-09-07 M. A. Bezuglov , A. I. Onishchenko

We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple…

High Energy Physics - Theory · Physics 2017-12-06 Zvi Bern , Michael Enciso , Harald Ita , Mao Zeng