PT Journal
AU Aguilera-Verdugo, JJ
   Hernandez-Pinto, RJ
   Rodrigo, G
   Sborlini, GFR
   Torres Bobadilla, WJ
TI Causal representation of multi-loop Feynman integrands within the loop-tree duality
SO Journal of High Energy Physics
JI J. High Energy Phys.
PY 2021
BP 69 - 26pp
VL 01
IS 1
DI 10.1007/JHEP01(2021)069
LA English
DE Duality in Gauge Field Theories; Perturbative QCD; Scattering Amplitudes
AB 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.
ER