期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP01(2021)069
关键词
Duality in Gauge Field Theories; Perturbative QCD; Scattering Amplitudes
资金
- Spanish Government (Agencia Estatal de Investigacion)
- ERDF funds from European Commission [FPA2017-84445-P]
- Generalitat Valenciana [GRISOLIAP/2018/101, PROMETEO/2017/053]
- COST Action [CA16201 PARTICLEFACE]
- Departament de Fisica Teorica, Universitat de Valencia
- CONACyT [A1-S-33202]
- Juan de la Cierva program [FJCI-2017-32128]
- Sistema Nacional de Investigadores
The paper discusses the application of loop-tree duality in multi-loop Feynman integrals, studying the dual representation of integrals generated from three parent topologies to provide very compact and causal integrand representations. Numerical integrations show the smooth behavior of dual expressions in integer space-time dimensions.
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.
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