Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2021)183
Keywords
NLO Computations; QCD Phenomenology
Categories
Funding
- COST Action [CA16201 PARTICLEFACE]
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The causal representation of multi-loop scattering amplitudes obtained from the loop-tree duality formalism provides a comprehensive understanding of the behavior of physical singularities at the integrand level. The study reveals compact expressions for multi-loop topologies with the same number of vertices and shows a correspondence between vertices and the collection of internal lines. By considering the structure of causal propagators, the paper presents explicit causal representations of loop topologies with up to nine vertices.
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.
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