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Related papers: Five-loop massless propagator integrals

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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

We summarize the results for the master integrals of the three-loop quark and gluon form factor in massless QCD. Working in dimensional regularization we extract poles up to 1/epsilon^6. The computational techniques involve, among others,…

High Energy Physics - Phenomenology · Physics 2010-01-20 T. Huber

For certain dimensionally-regulated massive two- and three-loop propagator-type diagrams the higher order epsilon-expansion is constructed.

High Energy Physics - Phenomenology · Physics 2010-04-05 M. Yu. Kalmykov

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of…

High Energy Physics - Phenomenology · Physics 2009-11-07 Thomas Becher , Kirill Melnikov

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…

High Energy Physics - Theory · Physics 2019-05-21 A. V. Kotikov , S. Teber

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

Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…

High Energy Physics - Phenomenology · Physics 2009-10-31 Francesco Caravaglios

The four-loop, two-point form factor contains the first non-planar correction to the lightlike cusp anomalous dimension. This anomalous dimension is a universal function which appears in many applications. Its planar part in N = 4 SYM is…

High Energy Physics - Theory · Physics 2016-01-19 Rutger Boels , Bernd A. Kniehl , Gang Yang

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary…

High Energy Physics - Phenomenology · Physics 2021-10-18 Dhimiter D. Canko , Costas G. Papadopoulos , Nikolaos Syrrakos

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal…

High Energy Physics - Theory · Physics 2008-11-26 Z. Bern , J. J. M. Carrasco , H. Johansson , D. A. Kosower

The perturbative expansion of two-point functions of lowest dimension supersymmetric operators in $\mathcal{N}=4$ SYM and ABJM theory exhibits uniform transcendental weight. Inspired by this, we construct an explicit basis of uniformly…

High Energy Physics - Theory · Physics 2025-12-15 Marco S. Bianchi

We compute the master integrals for massless two-loop vertex graphs with three off-shell legs. These master integrals are relevant for the QCD corrections to H to V*V* (where V = W, Z) and for two-loop studies of the triple gluon (and…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. G. Birthwright , E. W. N. Glover , P. Marquard

We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…

High Energy Physics - Phenomenology · Physics 2024-12-31 Samuel Abreu , Pier Francesco Monni , Ben Page , Johann Usovitsch

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

The \sqrt\epsilon-expansions for critical exponents of the weakly-disordered Ising model are calculated up to the five-loop order and found to possess coefficients with irregular signs and values. The estimate n_c = 2.855 for the marginal…

Statistical Mechanics · Physics 2009-10-31 B. N. Shalaev , S. A. Antonenko , A. I. Sokolov

We study the three-loop four-point amplitude in ABJM theory. We determine the dual conformal invariant integrals with highest number of propagators and fix their coefficients by two-particle cuts. Evaluating such a combination of integrals…

High Energy Physics - Theory · Physics 2015-06-19 Marco S. Bianchi , Matias Leoni

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 calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…

High Energy Physics - Theory · Physics 2026-05-19 Andrei V. Belitsky , Leonid V. Bork , Roman N. Lee , Andrei I. Onishchenko , Vladimir A. Smirnov

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional…

High Energy Physics - Phenomenology · Physics 2008-11-26 Charalampos Anastasiou , Ruth Britto , Bo Feng , Zoltan Kunszt , Pierpaolo Mastrolia

We present analytical expressions for the 31 five-particle phase-space master integrals in massless QCD as an $\epsilon$-series with coefficients being multiple zeta values of weight up to 12. In addition, we provide computer code for the…

High Energy Physics - Phenomenology · Physics 2018-08-01 O. Gituliar , V. Magerya , A. Pikelner