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Related papers: Attacking One-loop Multi-leg Feynman Integrals wit…

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Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed…

We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…

High Energy Physics - Phenomenology · Physics 2009-12-18 Wolfgang Kilian , Tobias Kleinschmidt

We present a new algorithm for the reduction of one-loop \emph{tensor} Feynman integrals with $n\leq 4$ external legs to \emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l \geq 0$ and…

High Energy Physics - Phenomenology · Physics 2011-04-20 Jochem Fleischer , Tord Riemann

The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…

High Energy Physics - Phenomenology · Physics 2017-04-05 Amedeo Primo , Lorenzo Tancredi

We describe the calculation of the one-loop corrections to $H \to \gamma \gamma$ and $g g \to H$ within the four-dimensional unsubtraction/loop-tree duality (FDU/LTD) approach. The fact that these corrections are both IR and UV finite is…

High Energy Physics - Phenomenology · Physics 2017-09-29 German F. R. Sborlini , Felix Driencourt-Mangin , German Rodrigo

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

High Energy Physics - Phenomenology · Physics 2011-09-21 F. Yuasa , T. Ishikawa , Y. Kurihara , J. Fujimoto , Y. Shimizu , N. Hamaguchi , E. de Doncker , K. Kato

Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies…

High Energy Physics - Phenomenology · Physics 2022-11-08 Selomit Ramírez-Uribe , Roger J. Hernández-Pinto , Germán Rodrigo , German F. R. Sborlini

In the past years, we have been developing a novel technique, called Four-Dimensional Unsubtraction (FDU) which aims to obtain purely four-dimensional representations of the matrix elements contributing to physical observables. In this…

High Energy Physics - Phenomenology · Physics 2019-11-05 German F. R. Sborlini

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…

High Energy Physics - Phenomenology · Physics 2013-12-16 T. Binoth , J. Ph. Guillet , G. Heinrich , E. Pilon , C. Schubert

In this talk we describe our approach for the computation of multi-leg one-loop amplitudes and present some first results relevant for LHC phenomenology.

High Energy Physics - Phenomenology · Physics 2009-11-11 T. Binoth , A. Guffanti , J. -Ph. Guillet , S. Karg , N. Kauer , T. Reiter

An efficient numerical algorithm to evaluate one-loop amplitudes using tensor integrals is presented. In particular, it is shown by explicit calculations that for ordered QCD amplitudes with a number of external legs up to 10, its…

High Energy Physics - Phenomenology · Physics 2009-08-11 A. van Hameren

We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…

High Energy Physics - Phenomenology · Physics 2015-06-16 P. Mastrolia , E. Mirabella , G. Ossola , T. Peraro

We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $\epsilon$-form, we manage to obtain a simple one-fold integral representation exact in…

High Energy Physics - Phenomenology · Physics 2016-03-23 Mikhail G. Kozlov , Roman N. Lee

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences…

High Energy Physics - Phenomenology · Physics 2009-11-10 W. T. Giele , E. W. N. Glover

In this paper, I present a technique to simplify the tensorial reduction of one-loop integrals with arbitrary internal masses, but at least two massless external legs. By applying the method to rank l tensor integrals, one ends up with at…

High Energy Physics - Phenomenology · Physics 2009-10-28 R. Pittau

I give an efficient algorithm for the reduction of multi-leg one-loop integrals of rank one. The method combines the basic ideas of the spinor algebra approach with the dual vector approach and is applicable to box integrals or higher point…

High Energy Physics - Phenomenology · Physics 2009-10-31 S. Weinzierl

A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is…

High Energy Physics - Phenomenology · Physics 2012-10-08 A. Freitas

The loop-tree duality (LTD) theorem establishes that loop contributions to scattering amplitudes can be computed through dual integrals, which are build from single cuts of the virtual diagrams. In order to build a complete LTD…

High Energy Physics - Phenomenology · Physics 2017-11-22 N. Selomit Ramírez-Uribe , Roger J. Hernández-Pinto , Germán Rodrigo

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 apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of…

High Energy Physics - Theory · Physics 2015-06-18 Johannes M. Henn , Alexander V. Smirnov , Vladimir A. Smirnov