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Related papers: Massive two-loop four-point Feynman integrals at h…

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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 apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of…

High Energy Physics - Phenomenology · Physics 2019-02-22 Go Mishima

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

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

High Energy Physics - Phenomenology · Physics 2009-10-28 Adrian Ghinculov

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a…

High Energy Physics - Phenomenology · Physics 2011-07-13 Alexey Pak , Alexander Smirnov

In this work, we investigate the finite basis topologies of two-loop dimensionally regularized Feynman integrals in the `t Hooft-Veltman scheme in the Standard Model. We present a functionally distinct finite basis of Master Integrals which…

High Energy Physics - Theory · Physics 2025-03-28 Piotr Bargiela , Tong-Zhi Yang

Feynman amplitudes at higher orders in perturbation theory generically have complex singular structures. Notwithstanding the emergence of many powerful new methods, the presence of infrared divergences poses significant challenges for their…

High Energy Physics - Phenomenology · Physics 2019-09-04 Charalampos Anastasiou , George Sterman

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us…

High Energy Physics - Theory · Physics 2026-02-24 Sid Smith

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…

High Energy Physics - Phenomenology · Physics 2015-06-19 Jakob Ablinger , Johannes Blümlein , Clemens Raab , Carsten Schneider , Fabian Wißbrock

In this paper we continue the work begun in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the…

High Energy Physics - Phenomenology · Physics 2009-02-11 S. Laporta

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends…

Algebraic Geometry · Mathematics 2009-03-24 Francis Brown

We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully…

High Energy Physics - Theory · Physics 2018-09-11 Janko Boehm , Alessandro Georgoudis , Kasper J. Larsen , Hans Schoenemann , Yang Zhang

Feynman integral reduction by means of integration-by-parts identities is a major power gadget in a theorist toolbox indispensable for calculation of multiloop quantum effects relevant for particle phenomenology and formal theory alike. An…

High Energy Physics - Phenomenology · Physics 2024-02-13 A. V. Belitsky , A. A. Kokosinskaya , A. V. Smirnov , V. V. Voevodin , M. Zeng

We present an analytic calculation of three-loop four-point Feynman integrals with two off-shell legs of equal mass. We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical…

High Energy Physics - Phenomenology · Physics 2024-12-24 Ming-Ming Long

We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass…

High Energy Physics - Phenomenology · Physics 2008-11-26 A. Denner , S. Pozzorini

In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the…

High Energy Physics - Theory · Physics 2023-09-12 Xuhang Jiang , Xing Wang , Li Lin Yang , Jingbang Zhao

We discuss two-loop leading and angular-dependent next-to-leading logarithmic electroweak virtual corrections to arbitrary processes at energies above the electroweak scale. The relevant Feynman diagrams involving soft-collinear gauge…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ansgar Denner , Michael Melles , Stefano Pozzorini

Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found…

High Energy Physics - Theory · Physics 2026-03-31 Gwenaël Ferrando , Florian Loebbert , Amelie Pitters , Sven F. Stawinski

We investigate a novel theoretical structure underlying the computation of integration-by-parts relations between Feynman integrals via syzygy-based methods. Building on insights from intersection theory, we analyze the large-$\epsilon$…

High Energy Physics - Theory · Physics 2025-09-23 Ben Page , Qian Song

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