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Related papers: Evaluating double and triple (?) boxes

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An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…

High Energy Physics - Phenomenology · Physics 2018-09-26 Sophia Borowka , Thomas Gehrmann , Daniel Hulme

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 method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop non-planar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the…

High Energy Physics - Theory · Physics 2021-11-03 B. Ananthanarayan , Abhijit B. Das , Daniel Wyler

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

We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of…

High Energy Physics - Theory · Physics 2023-06-05 Andrew McLeod , Roger Morales , Matt von Hippel , Matthias Wilhelm , Chi Zhang

Two recently developed techniques of analytic evaluation of multifold Mellin-Barnes (MB) integrals are presented. Both approaches rest on the definition of geometrical objets conveniently associated with the MB integrands, which can then be…

High Energy Physics - Theory · Physics 2024-02-07 Sumit Banik , Samuel Friot

The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Gehrmann , E. Remiddi

The high-energy behaviour of scattering amplitudes involving massive particles has attracted interest in recent years. In these proceedings, we report on the analytic tool AsyInt for solving massive multi-loop Feynman integrals in the…

High Energy Physics - Phenomenology · Physics 2025-10-14 Hantian Zhang

Evidence has recently emerged for a hidden symmetry of scattering amplitudes in N=4 super Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong…

High Energy Physics - Theory · Physics 2008-11-26 Dung Nguyen , Marcus Spradlin , Anastasia Volovich

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1…

High Energy Physics - Theory · Physics 2016-08-29 Rodrigo Turcati , Mário Júnior Neves

We derive the (matrix-valued) Feynman rules of mass perturbation theory of the massive Schwinger model for non-zero vacuum angle theta. Further, we discuss the properties of the three-boson bound state and compute -- by a partial…

High Energy Physics - Theory · Physics 2009-07-24 C. Adam

Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.

High Energy Physics - Phenomenology · Physics 2009-10-31 J. Fleischer , M. Yu. Kalmykov , A. V. Kotikov

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…

High Energy Physics - Phenomenology · Physics 2025-12-17 Claude Duhr , Paul Mork

One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…

High Energy Physics - Theory · Physics 2008-11-26 A. T. Suzuki , A. G. M. Schmidt

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type…

High Energy Physics - Phenomenology · Physics 2015-06-22 Stefano Di Vita , Pierpaolo Mastrolia , Ulrich Schubert , Valery Yundin

We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly…

High Energy Physics - Theory · Physics 2025-04-17 Burkhard Eden

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…

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

We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges or when removing them by putting them on…

High Energy Physics - Theory · Physics 2023-02-27 Marko Berghoff , Dirk Kreimer

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…

High Energy Physics - Theory · Physics 2011-09-13 A. T. Suzuki , E. S. Santos , A. G. M. Schmidt

We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral…

High Energy Physics - Phenomenology · Physics 2009-11-10 G. Duplancic , B. Nizic