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We determine the complete three-loop QCD soft anomalous dimension for multileg amplitudes involving a single massive coloured particle and any number of massless ones. This is achieved by applying a novel strategy based on a lightcone…

High Energy Physics - Phenomenology · Physics 2025-11-03 Einan Gardi , Zehao Zhu

We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and…

High Energy Physics - Phenomenology · Physics 2022-05-04 J. Blümlein , P. Marquard , C. Schneider , K. Schönwald

Graphics Processing Units (GPUs) are employed for a numerical determination of the analytic structure of two-point correlation functions of Quantum Field Theories. These functions are represented through integrals in d-dimensional Euclidean…

High Energy Physics - Phenomenology · Physics 2013-01-16 Andreas Windisch , Reinhard Alkofer , Gundolf Haase , Manfred Liebmann

We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N=4 SYM, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is…

High Energy Physics - Theory · Physics 2021-10-13 Yuanhong Guo , Lei Wang , Gang Yang

The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for $W$-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a…

High Energy Physics - Phenomenology · Physics 2024-09-16 Wen-Jie He , Ren-You Zhang , Liang Han , Yi Jiang , Zhe Li , Xiao-Feng Wang , Shu-Xiang Li , Pan-Feng Li , Qing-hai Wang

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

An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…

Computational Physics · Physics 2007-05-23 A. A. Zhmudsky

Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman…

High Energy Physics - Theory · Physics 2024-04-15 Lecheng Ren , Marcus Spradlin , Cristian Vergu , Anastasia Volovich

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the…

High Energy Physics - Phenomenology · Physics 2019-12-13 Matteo Becchetti , Roberto Bonciani , Valerio Casconi , Andrea Ferroglia , Simone Lavacca , Andreas von Manteuffel

In this contribution, we present a recently introduced approach [BorkLeeOnishchenko2025] to the calculation of slightly off-shell dual conformal integrals based on the method of regions with regularization preserving dual conformal…

High Energy Physics - Phenomenology · Physics 2026-03-05 Roman N. Lee

Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the…

Disordered Systems and Neural Networks · Physics 2009-10-30 Imre Varga , Etienne Hofstetter , Janos Pipek

We present differential equations (DEs) in canonical form for a family of two-loop five-point Feynman integrals containing elliptic functions and nested square roots. This is the only family for which canonical DEs were not yet available…

High Energy Physics - Theory · Physics 2025-08-22 Matteo Becchetti , Christoph Dlapa , Simone Zoia

We present the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric integrations for a basis of finite integrals, we give…

High Energy Physics - Phenomenology · Physics 2019-07-22 Andreas von Manteuffel , Robert M. Schabinger

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

Classical Analysis and ODEs · Mathematics 2026-05-28 K. Castillo

The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman…

High Energy Physics - Phenomenology · Physics 2007-05-23 Michele Caffo

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…

High Energy Physics - Phenomenology · Physics 2023-03-29 Stephen P. Martin

We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We…

High Energy Physics - Theory · Physics 2010-01-15 Tigran Hakobyan , Sergey Krivonos , Olaf Lechtenfeld , Armen Nersessian

We present analytic results of the two-loop master integrals for hadronic $tW$ production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in…

High Energy Physics - Phenomenology · Physics 2023-02-17 Jian Wang , Yefan Wang

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…

High Energy Physics - Phenomenology · Physics 2018-07-17 J. Blümlein , A. De Freitas , M. van Hoeij , E. Imamoglu , P. Marquard , C. Schneider

Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite…

Mathematical Physics · Physics 2015-05-28 Satoru Odake , Ryu Sasaki