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Related papers: Three-loop master integrals for ladder-box diagram…

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3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation…

High Energy Physics - Phenomenology · Physics 2015-06-05 Jakob Ablinger , Johannes Blümlein , Alexander Hasselhuhn , Sebastian Klein , Carsten Schneider , Fabian Wißbrock

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…

High Energy Physics - Phenomenology · Physics 2013-08-26 Thomas Gehrmann , Lorenzo Tancredi , Erich Weihs

We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg to arbitrary order in the dimensional regulator in $d=4-2\epsilon$ space-time dimensions. A pure basis of Master…

High Energy Physics - Phenomenology · Physics 2021-06-23 Nikolaos Syrrakos

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

We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…

High Energy Physics - Phenomenology · Physics 2015-05-20 Tobias Huber , Susanne Krankl

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.

High Energy Physics - Phenomenology · Physics 2017-08-18 B. A. Kniehl , A. F. Pikelner , O. L. Veretin

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…

High Energy Physics - Phenomenology · Physics 2025-12-17 Claude Duhr , Paul Mork

We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are…

High Energy Physics - Phenomenology · Physics 2022-10-12 Stefano Di Vita , Thomas Gehrmann , Stefano Laporta , Pierpaolo Mastrolia , Amedeo Primo , Ulrich Schubert

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…

High Energy Physics - Phenomenology · Physics 2014-06-13 Thomas Gehrmann , Andreas von Manteuffel , Lorenzo Tancredi , Erich Weihs

We study the scalar and tensor integrals associated with the pentabox topology: the class of two-loop box integrals with seven propagators - five in one loop and three in the other. We focus on the case where the external legs are…

High Energy Physics - Phenomenology · Physics 2008-11-26 C. Anastasiou , E. W. N. Glover , C. Oleari

We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…

High Energy Physics - Phenomenology · Physics 2018-02-28 Xiao Liu , Yan-Qing Ma , Chen-Yu Wang

In this article we present a high-precision evaluation of the expansions in $\e=(4-d)/2$ of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of…

High Energy Physics - Phenomenology · Physics 2009-11-11 Y. Schroder , A. Vuorinen

We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the…

High Energy Physics - Phenomenology · Physics 2024-05-01 Simon Badger , Matteo Becchetti , Nicolò Giraudo , Simone Zoia

In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234. We compute the integrals by defining differential…

High Energy Physics - Phenomenology · Physics 2020-07-15 Hjalte Frellesvig , Martijn Hidding , Leila Maestri , Francesco Moriello , Giulio Salvatori

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Diakonidis , J. Fleischer , J. Gluza , K. Kajda , T. Riemann , J. B. Tausk

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of…

High Energy Physics - Phenomenology · Physics 2009-12-30 S. Groote , J. G. Körner , A. A. Pivovarov

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a…

Mathematical Physics · Physics 2015-05-18 Ian Marquette

The $tW$ associated production has the second-largest cross section among three single top production channels. A complete study of NNLO QCD corrections to $tW$ production is still missing in literature. We present the calculation of part…

High Energy Physics - Phenomenology · Physics 2021-11-30 Ming-Ming Long , Ren-You Zhang , Wen-Gan Ma , Yi Jiang , Liang Han , Zhe Li , Shuai-Shuai Wang

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…

High Energy Physics - Phenomenology · Physics 2009-10-31 T. Binoth , G. Heinrich

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that…

High Energy Physics - Phenomenology · Physics 2009-11-07 Stefano Laporta