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Related papers: Loop-tree duality from vertices and edges

200 papers

We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…

High Energy Physics - Phenomenology · Physics 2010-12-13 Isabella Bierenbaum

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…

High Energy Physics - Phenomenology · Physics 2015-06-19 Sebastian Buchta , Grigorios Chachamis , Petros Draggiotis , Ioannis Malamos , German Rodrigo

We present the first proof-of-concept application to decay processes at higher perturbative orders of LTD causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the loop-tree duality (LTD) and is…

We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multiloop integrals derived in previous…

High Energy Physics - Phenomenology · Physics 2012-11-22 Isabella Bierenbaum , Sebastian Buchta , Petros Draggiotis , Ioannis Malamos , German Rodrigo

We review the structure of gauge theory scattering amplitudes at tree level and describe how a compact expression can be found which encodes all the tree-level amplitudes in the maximally supersymmetric N=4 theory. The expressions for the…

High Energy Physics - Theory · Physics 2015-05-28 J. M. Drummond

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

The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the…

Loop-Tree Duality (LTD) is a framework in which the energy components of all loop momenta of a Feynman integral are integrated out using residue theorem, resulting in a sum over tree-like structures. Originally, the LTD expression exhibits…

High Energy Physics - Phenomenology · Physics 2020-09-28 Zeno Capatti , Valentin Hirschi , Dario Kermanschah , Andrea Pelloni , Ben Ruijl

The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting…

High Energy Physics - Phenomenology · Physics 2021-01-27 Felix Driencourt-Mangin , German Rodrigo , German F. R. Sborlini , William J. Torres Bobadilla

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

High Energy Physics - Theory · Physics 2016-12-28 Harald Ita

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

The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g.…

High Energy Physics - Theory · Physics 2026-02-23 James Drummond , Matthew Rochford , Rowan Wright

This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$\phi^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the…

High Energy Physics - Theory · Physics 2024-10-01 Nima Arkani-Hamed , Hadleigh Frost , Giulio Salvatori , Pierre-Guy Plamondon , Hugh Thomas

An overview of a quantum algorithm application for the identification of causal singular configurations of multiloop Feynman diagrams is presented. The quantum algorithm is implemented in two different quantum simulators, the output…

High Energy Physics - Phenomenology · Physics 2022-01-13 Selomit Ramírez-Uribe

Loop-tree duality allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct comparison with real radiation terms. In this talk, we review the basis of the method and describe its application to…

High Energy Physics - Phenomenology · Physics 2016-01-21 German F. R. Sborlini

Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show…

High Energy Physics - Phenomenology · Physics 2020-07-01 Robert Runkel , Zoltán Szőr , Juan Pablo Vesga , Stefan Weinzierl

We review the recent progress on the numerical implementation of the Loop-Tree Duality Method (LTDM) for the calculation of scattering amplitudes. A central point is the analysis of the singularities of the integrand. In the framework of…

High Energy Physics - Phenomenology · Physics 2015-09-25 Sebastian Buchta , Grigorios Chachamis , Petros Draggiotis , Ioannis Malamos , 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 extend useful properties of the $H\to\gamma\gamma$ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form -- regardless of the…

High Energy Physics - Phenomenology · Physics 2019-03-27 Felix Driencourt-Mangin , German Rodrigo , German F. R. Sborlini , William J. Torres Bobadilla

Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…

Discrete Mathematics · Computer Science 2025-10-28 Naveed Ahmed Azam , Seemab Hayat