English
Related papers

Related papers: Numerical Evaluation of Feynman Loop Integrals by …

200 papers

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…

High Energy Physics - Phenomenology · Physics 2023-05-22 Ramon Winterhalder , Vitaly Magerya , Emilio Villa , Stephen P. Jones , Matthias Kerner , Anja Butter , Gudrun Heinrich , Tilman Plehn

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…

High Energy Physics - Phenomenology · Physics 2008-11-26 G. Passarino

We present a first numerical implementation of the Loop-Tree Duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a…

High Energy Physics - Phenomenology · Physics 2015-10-06 Sebastian Buchta , Grigorios Chachamis , Petros Draggiotis , German Rodrigo

The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level scattering amplitudes. This is achieved by directly applying the Residue Theorem to the loop-energy-integration.…

High Energy Physics - Phenomenology · Physics 2015-09-25 Sebastian Buchta

This paper describes a method of numerical evaluating high-order QED contributions to the electron anomalous magnetic moment. The method is based on subtraction of infrared and ultraviolet divergences in Feynman-parametric space before…

High Energy Physics - Phenomenology · Physics 2018-11-07 Sergey Volkov

One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…

High Energy Physics - Theory · Physics 2023-09-27 German F. R. Sborlini

In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…

High Energy Physics - Phenomenology · Physics 2024-09-12 German Sborlini

Loop-tree duality (LTD) allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct mapping with real radiation terms. We review the basis of the method and describe its application to regularize…

High Energy Physics - Phenomenology · Physics 2015-10-19 German F. R. Sborlini , Roger Hernandez-Pinto , German Rodrigo

We investigate relations between loop and tree amplitudes in quantum field theory that involve putting on-shell some loop propagators. This generalizes the so-called Feynman tree theorem which is satisfied at 1-loop. Exploiting retarded…

High Energy Physics - Phenomenology · Physics 2011-05-23 Simon Caron-Huot

We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…

High Energy Physics - Phenomenology · Physics 2017-11-08 Andreas von Manteuffel , Robert M. Schabinger

This paper presents a new method of numerical computation of the QED contributions to the electron anomalous magnetic moment which arises from Feynman graphs containing electron and photon lines and not containing electron loops. The method…

High Energy Physics - Phenomenology · Physics 2017-11-29 Sergey Volkov

We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its…

High Energy Physics - Phenomenology · Physics 2010-11-03 Isabella Bierenbaum , Stefano Catani , Petros Draggiotis , German Rodrigo

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…

High Energy Physics - Phenomenology · Physics 2020-11-24 Zeno Capatti , Valentin Hirschi , Dario Kermanschah , Andrea Pelloni , Ben Ruijl

One approach to the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order is to perform all of the integrations, including the virtual loop integration, by Monte Carlo numerical…

High Energy Physics - Phenomenology · Physics 2010-04-14 Wei Gong , Zoltan Nagy , Davison E. Soper

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

High Energy Physics - Phenomenology · Physics 2014-11-20 Ayres Freitas , Yi-Cheng Huang

We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that…

High Energy Physics - Phenomenology · Physics 2014-07-23 Sebastian Buchta , Grigorios Chachamis , Ioannis Malamos , Isabella Bierenbaum , Petros Draggiotis , German Rodrigo

Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree…

We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an…

High Energy Physics - Phenomenology · Physics 2010-10-27 Charalampos Anastasiou , Stefan Beerli , Alejandro Daleo

In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids…

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…

High Energy Physics - Phenomenology · Physics 2025-11-21 Tommaso Armadillo