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The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…

High Energy Physics - Phenomenology · Physics 2010-04-05 T. Gehrmann , G. Heinrich , T. Huber , C. Studerus

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…

High Energy Physics - Phenomenology · Physics 2015-06-03 Robert M. Schabinger

The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then…

High Energy Physics - Theory · Physics 2007-05-23 M. Caffo , H. Czyz , S. Laporta , E. Remiddi

We consider the anomalous dimension of the flavor non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in QCD and construct its contribution proportional to zeta(3) in analytic form by applying advanced methods of…

High Energy Physics - Phenomenology · Physics 2025-03-27 B. A. Kniehl , V. N. Velizhanin

We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby…

High Energy Physics - Theory · Physics 2013-10-18 Mads Sogaard

We study the flavorless gluon propagator in the Landau gauge from high statistics lattice calculations. Hypercubic artifacts are efficiently eliminated by taking the $\sum p_\mu^4 \to 0$ limit. The propagator is fitted to the three-loops…

High Energy Physics - Phenomenology · Physics 2010-03-19 D. Becirevic , Ph. Boucaud , J. P. Leroy , J. Micheli , O. Pene , J. Rodriguez-Quintero , C. Roiesnel

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

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…

High Energy Physics - Phenomenology · Physics 2011-09-29 T. Gehrmann , E. Remiddi

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of…

Mathematical Physics · Physics 2009-11-11 Siu A. Chin

The massless S-matrix of the pure RR AdS3 X S3 X T4 theory is very similar but not quite the same as Fendley-Intriligator's N=2 S-matrix, in turns related to Sine-Gordon taken at a special coupling. In this short note we review the reason…

High Energy Physics - Theory · Physics 2026-01-21 Alessandro Torrielli

We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight…

High Energy Physics - Phenomenology · Physics 2021-09-14 Nikolaos Syrrakos

We explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The…

High Energy Physics - Theory · Physics 2016-12-30 Mads Sogaard , Yang Zhang

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master…

High Energy Physics - Phenomenology · Physics 2015-06-04 Pierpaolo Mastrolia , Edoardo Mirabella , Tiziano Peraro

Motivated by the foundational work of Tarasov, who pointed out that the algebraic relations of the type considered here can lead to functional reduction of Feynman integrals, we suitably modify the original method to be able to implement…

High Energy Physics - Phenomenology · Physics 2023-09-14 B. Ananthanarayan , Souvik Bera , Tanay Pathak

Using the integration by parts method we derive a closed analytical expression for the result of the integration of an arbitrary dimensionally regulated tadpole diagram composed of a massless propagator and two massive ones, each raised…

High Energy Physics - Phenomenology · Physics 2007-05-23 K. G. Chetyrkin

The method of dimensional recurrences proposed by one of the authors [1,2] is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result…

High Energy Physics - Theory · Physics 2015-05-18 Bernd A. Kniehl , Oleg V. Tarasov

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 present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…

High Energy Physics - Phenomenology · Physics 2019-11-22 Robert Runkel , Zoltán Szőr , Juan Pablo Vesga , Stefan Weinzierl

A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail. The method is based on a repeated application of the functional relations proposed by the author.…

High Energy Physics - Phenomenology · Physics 2022-07-13 O. V. Tarasov

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