TY  - JOUR
AU  - Aguilera-Verdugo, J. J.
AU  - Hernandez-Pinto, R. J.
AU  - Rodrigo, G.
AU  - Sborlini, G. F. R.
AU  - Torres Bobadilla, W. J.
PY  - 2021
DA  - 2021//
TI  - Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
T2  - J. High Energy Phys.
JO  - Journal of High Energy Physics
SP  - 112
EP  - 42pp
VL  - 02
IS  - 2
PB  - Springer
KW  - NLO Computations
KW  - QCD Phenomenology
AB  - The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the novel integrand-level representation of Feynman integrals, which is based on the Loop-Tree Duality (LTD). We explore the behaviour of the multi-loop iterated residues and explicitly show, by developing a general compact and elegant proof, that contributions associated to displaced poles are cancelled out. The remaining residues, called nested residues as originally introduced in ref. [1], encode the relevant physical information and are naturally mapped onto physical configurations associated to nondisjoint on-shell states. By going further on the mathematical structure of the nested residues, we prove that unphysical singularities vanish, and show how the final expressions can be written by using only causal denominators. In this way, we provide a mathematical proof for the all-loop formulae presented in ref. [2].
SN  - 1029-8479
UR  - https://arxiv.org/abs/2010.12971
UR  - https://doi.org/10.1007/JHEP02(2021)112
DO  - 10.1007/JHEP02(2021)112
LA  - English
N1  - WOS:000620526300001
ID  - Aguilera-Verdugo_etal2021
ER  -