Causal representation of multi-loop Feynman integrands within the loop-tree duality

A bstract The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these tw...

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Bibliographic Details
Published in:The journal of high energy physics 2021-01, Vol.2021 (1), p.1-26, Article 69
Main Authors: Aguilera-Verdugo, J. Jesús, Hernández-Pinto, Roger J., Rodrigo, Germán, Sborlini, German F. R., Torres Bobadilla, William J.
Format: Article
Language:English
Subjects:
Algorithms
Classical and Quantum Gravitation
Duality in Gauge Field Theories
Elementary Particles
Euclidean space
Fields (mathematics)
High energy physics
Integrals
Perturbative QCD
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Representations
Scattering Amplitudes
Singularities
Spacetime
String Theory
Topology
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Summary:A bstract The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2021)069