Loop-tree duality from vertices and edges

A bstract The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for mu...

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Bibliographic Details
Published in:The journal of high energy physics 2021-04, Vol.2021 (4), p.1-28, Article 183
Main Author: Torres Bobadilla, William J.
Format: Article
Language:English
Subjects:
Apexes
Classical and Quantum Gravitation
Elementary Particles
Euclidean space
Graph theory
High energy physics
Integrals
NLO Computations
Physics
Physics and Astronomy
QCD Phenomenology
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Representations
String Theory
Topology
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Summary:A bstract The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of vertices . Interestingly, integrands considered in former studies, with up-to six vertices and L internal lines, display the same structure of up-to four-loop ones. The former is an insight that there should be a correspondence between vertices and the collection of internal lines, edges , that characterise a multi-loop topology. By virtue of this relation, in this paper, we embrace an approach to properly classify multi-loop topologies according to vertices and edges. Differently from former studies, we consider the most general topologies, by connecting vertices and edges in all possible ways. Likewise, we provide a procedure to generate causal representation of multi-loop topologies by considering the structure of causal propagators. Explicit causal representations of loop topologies with up-to nine vertices are provided.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2021)183