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Related papers: Planar master integrals for four-loop form factors

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The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…

High Energy Physics - Phenomenology · Physics 2009-10-28 Arttu K. Rajantie

The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. \cite{Behring:2023rlq,Ablinger:2023ahe}. They…

High Energy Physics - Phenomenology · Physics 2024-05-15 J. Ablinger , A. Behring , J. Blümlein , A. De Freitas , A. von Manteuffel , C. Schneider , K. Schönwald

We obtain for the first time the analytic two-loop four-point MHV lightlike form factor of the stress-tensor supermultiplet in planar ${\cal N}=4$ SYM where the momentum $q$ carried by the operator is taken to be massless. Remarkably, we…

High Energy Physics - Theory · Physics 2025-03-11 Yuanhong Guo , Lei Wang , Gang Yang

We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity…

High Energy Physics - Theory · Physics 2016-08-24 Dmitry Chicherin , James Drummond , Paul Heslop , Emery Sokatchev

We report on the three-loop unpolarized and polarized massive operator matrix elements, with single- and two-mass corrections, and the associated deep-inelastic massive Wilson coefficients in the region $Q^2 \gg m_Q^2$, the calculation of…

High Energy Physics - Phenomenology · Physics 2026-02-12 J. Ablinger , A. Behring , J. Blümlein , A. De Freitas , A. von Manteuffel , C. Schneider , K. Schönwald

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals,…

High Energy Physics - Phenomenology · Physics 2021-05-05 R. N. Lee , A. I. Onishchenko

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…

High Energy Physics - Phenomenology · Physics 2026-04-03 Yuanche Liu , Antonela Matijašić , Tiziano Peraro , Yingxuan Xu , Zihua Yang , Yang Zhang

We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…

High Energy Physics - Phenomenology · Physics 2011-09-13 Andre van Hameren , Jens Vollinga , Stefan Weinzierl

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

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…

High Energy Physics - Phenomenology · Physics 2009-11-07 S. Laporta

We derive the four-dimensional integrand of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. In our integrand…

High Energy Physics - Theory · Physics 2023-06-26 Tushar Gopalka , Enrico Herrmann

We evaluate the master integrals for the two-loop non-planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to-leading order in QED. We adopt the method of differential equations and the Magnus…

High Energy Physics - Phenomenology · Physics 2018-09-17 Stefano Di Vita , Stefano Laporta , Pierpaolo Mastrolia , Amedeo Primo , Ulrich Schubert

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master…

High Energy Physics - Phenomenology · Physics 2023-11-15 T. Gehrmann , E. W. N. Glover , T. Huber , N. Ikizlerli , C. Studerus

We explicitly compute the complete three-loop (O(g^4)) contribution to the four-point function of chiral primary current-like operators <(q)^2 q^2 (q)^2 q^2> in any finite N=2 SYM theory. The computation uses N=2 harmonic supergraphs in…

High Energy Physics - Theory · Physics 2009-10-31 B. Eden , C. Schubert , E. Sokatchev

Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…

High Energy Physics - Phenomenology · Physics 2024-10-01 Elise de Doncker , Tadashi Ishikawa , Kiyoshi Kato , Fukuko Yuasa

We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably simple and all integrals are expressed as linear combinations of iterated integrals…

High Energy Physics - Theory · Physics 2019-10-23 Johannes Broedel , Claude Duhr , Falko Dulat , Robin Marzucca , Brenda Penante , Lorenzo Tancredi

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

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 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

We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including…

High Energy Physics - Theory · Physics 2014-03-24 Erik Panzer