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Related papers: Master Integrals for Four-Loop Massless Form Facto…

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We compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results…

High Energy Physics - Phenomenology · Physics 2015-06-23 Guido Bell , Tobias Huber

Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…

High Energy Physics - Phenomenology · Physics 2011-03-02 J. FUJIMOTO , Y. SHIMIZU , K. KATO , T. KANEKO

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

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

All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs…

High Energy Physics - Phenomenology · Physics 2007-05-23 M. Czakon , J. Gluza , T. Riemann

We present novel techniques for the computation of three-loop four-parton scattering amplitudes in full color, non-planar gauge theories. We elaborate on how the analytic results for these amplitudes can be used to confirm the conjectured…

High Energy Physics - Phenomenology · Physics 2022-08-18 Amlan Chakraborty , Giulio Gambuti

We compute all the planar three-loop master integrals relevant for the leading colour N3LO QCD corrections to the production of two massive or off-shell vector bosons at hadron colliders. These integrals are organised into nine four-point…

High Energy Physics - Phenomenology · Physics 2026-05-27 Dhimiter Canko , Mattia Pozzoli

We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of 't Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical…

High Energy Physics - Phenomenology · Physics 2010-04-21 Dao Thi Nhung , Le Duc Ninh

We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of…

High Energy Physics - Theory · Physics 2015-06-18 Johannes M. Henn , Alexander V. Smirnov , Vladimir A. Smirnov

We present Forcer, a new FORM program for the calculation of four-loop massless propagators. The basic framework is similar to that of the Mincer program for three-loop massless propagators: the program reduces Feynman integrals to a set of…

High Energy Physics - Phenomenology · Physics 2016-12-21 T. Ueda , B. Ruijl , J. A. M. Vermaseren

We compute the three-loop non-singlet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective…

High Energy Physics - Phenomenology · Physics 2022-05-11 Matteo Fael , Fabian Lange , Kay Schoenwald , Matthias Steinhauser

Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave…

High Energy Physics - Phenomenology · Physics 2018-08-15 B. Ananthanarayan , Shayan Ghosh , Alexey Vladimirov , Daniel Wyler

To get the total cross section of one interaction from its amplitude ${\cal M}$, one needs to integrate $|{\cal M}|^2$ over phase spaces of all out-going particles. Starting from this paper, we will propose a new method to perform such…

High Energy Physics - Phenomenology · Physics 2010-04-06 Bo Feng , Rijun Huang , Yin Jia , Mingxing Luo , Honghui Wang

We analytically compute the four-loop QCD corrections for the colour structure $(d_F^{abcd})^2$ to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in…

High Energy Physics - Phenomenology · Physics 2019-03-27 Roman N. Lee , Alexander V. Smirnov , Vladimir A. Smirnov , Matthias Steinhauser

We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM. Both the leading-color and non-leading-color form factors are expanded in terms of simple integrals.…

High Energy Physics - Theory · Physics 2024-03-04 Xin Guan , Guanda Lin , Xiao Liu , Yan-Qing Ma , Gang Yang

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…

High Energy Physics - Phenomenology · Physics 2009-11-11 A. V. Bogdan , R. N. Lee

Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited…

High Energy Physics - Theory · Physics 2017-01-06 Florian Loebbert , Christoph Sieg , Matthias Wilhelm , Gang Yang

We have constructed an epsilon-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak rho-parameter. Using transformation rules from the…

High Energy Physics - Phenomenology · Physics 2008-11-26 M. Faisst , P. Maierhoefer , C. Sturm

We present the calculation of all non-planar master integrals that are needed to describe production of two off-shell vector bosons in collisions of two massless partons through NNLO in perturbative QCD. The integrals are computed…

High Energy Physics - Phenomenology · Physics 2015-06-19 Fabrizio Caola , Johannes M. Henn , Kirill Melnikov , Vladimir A. Smirnov