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Related papers: Differential equations for multi-loop integrals an…

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We continue the study of the duality between super-correlators and scattering super-amplitudes in planar N=4 SYM. We provide a number of further examples supporting the conjectured duality relation between these two seemingly different…

High Energy Physics - Theory · Physics 2015-05-27 Burkhard Eden , Paul Heslop , Gregory P. Korchemsky , Emery Sokatchev

We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…

High Energy Physics - Phenomenology · Physics 2009-11-11 Charalampos Anastasiou , Alejandro Daleo

We obtain the full-color four-loop three-point form factor of the stress-tensor supermultiplet in N=4 SYM, based on the color-kinematics (CK) duality and generalized unitarity method. The CK-dual solution, while manifesting all dual Jacobi…

High Energy Physics - Theory · Physics 2024-12-03 Guanda Lin , Gang Yang , Siyuan Zhang

This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…

Numerical Analysis · Mathematics 2008-07-03 Laurent Demanet , Lexing Ying

In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree…

High Energy Physics - Phenomenology · Physics 2018-01-10 William J. Torres Bobadilla

We perform extensive three-loop tests of the hexagon bootstrap approach for structure constants in planar $\mathcal{N}=4$ SYM theory. We focus on correlators involving two BPS operators and one non-BPS operator in the so-called $SL(2)$…

High Energy Physics - Theory · Physics 2015-10-07 Benjamin Basso , Vasco Goncalves , Shota Komatsu , Pedro Vieira

We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…

High Energy Physics - Phenomenology · Physics 2009-09-25 A. Frink , J. G. Körner , J. B. Tausk

We compute $\epsilon$-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is…

High Energy Physics - Theory · Physics 2019-01-04 Samuel Abreu , Ben Page , Mao Zeng

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 bootstrap the two-loop four-point next-to-maximally helicity-violating (NMHV) ratio function for the chiral stress-tensor form factor in planar maximally supersymmetric Yang-Mills theory (sYM) at the symbol level. Starting from an ansatz…

High Energy Physics - Theory · Physics 2026-05-29 Song He , Jiahao Liu , Qinglin Yang

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals…

High Energy Physics - Phenomenology · Physics 2015-06-18 Johannes M. Henn , Kirill Melnikov , Vladimir A. Smirnov

We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…

High Energy Physics - Phenomenology · Physics 2009-10-30 A. Ghinculov , Y. -P. Yao

We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.

High Energy Physics - Phenomenology · Physics 2007-05-23 A. V. Kotikov

We consider the recursion relation for loop integrands in planar N = 4 SYM generated by an all-line shift of momentum twistors. We examine the behaviour of the rational loop integrands when the shift parameter becomes large, and find that a…

High Energy Physics - Theory · Physics 2015-05-20 Mathew Bullimore

Prompted by recent progress in the study of N=4 super Yang-Mills amplitudes, and evidence that similar approaches might be relevant to N=8 supergravity, we investigate possible iterative structures and applications of Wilson loop techniques…

High Energy Physics - Theory · Physics 2008-11-26 Andreas Brandhuber , Paul Heslop , Adele Nasti , Bill Spence , Gabriele Travaglini

We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformally-regulated chiral integrands. The remainder function is obtained as part of the two-loop…

High Energy Physics - Theory · Physics 2020-03-18 Jacob L. Bourjaily , Matthias Volk , Matt von Hippel

We find that scattering amplitudes in massive scalar QCD can manifest the duality between color and kinematics at loop-level. Specifically we construct the one-loop integrands for four-point scattering between two distinct massive scalars,…

High Energy Physics - Theory · Physics 2021-02-10 John Joseph M. Carrasco , Ingrid A. Vazquez-Holm

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}=4$ super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms.…

High Energy Physics - Theory · Physics 2026-01-23 Lance J. Dixon , Shuo Xin

I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…

High Energy Physics - Phenomenology · Physics 2014-05-16 Johannes M. Henn

We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at four loops. A powerful…

High Energy Physics - Theory · Physics 2015-09-29 Lance J. Dixon , Matt von Hippel , Andrew J. McLeod