English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The computation of multi-loop multi-leg scattering amplitudes plays a keyrole to improve the precision of theoretical predictions for particle physicsat high-energy colliders. In this work, we focus on the mathematical propertiesof the novel integrand-level representation of Feynman integrals, which isbased on the Loop-Tree Duality (LTD). We explore the behaviour of themulti-loop iterated residues and explicitly show, by developing a generalformal proof for the first time, that contributions associated to displacedpoles are cancelled out. The remaining residues, called nested residues asoriginally introduced in Ref. \cite{Verdugo:2020kzh}, encode the relevantphysical information and are naturally mapped onto physical configurationsassociated to nondisjoint on-shell states. By going further on the mathematicalstructure of the nested residues, we prove that unphysical singularitiesvanish, and show how the final expressions can be written by using only causaldenominators. In this way, we provide a mathematical proof for the all-loopformulae presented in Ref. \cite{Aguilera-Verdugo:2020kzc}.

Mathematical properties of nested residues and their application to multi-loop scattering amplitudes