William J. Torres Bobadilla (Max Planck – Munich)

All loop causal representation of scattering amplitudes

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) formulation offers a powerful framework to easily characterise and distinguish these two types of singularities, and then analytically simplify the underlying expressions. On top of it, we elucidate that the causal representation of loop topologies depends only on the features of the latter, vertices and edges. In effect, by virtue of this relation, a straightforward classification of loop topologies in terms causal (physical) thresholds can be generated, regardless of the loop order. Finally, we introduce the Mathematica package Lotty that automates the LTD formulation at multi-loop level by means of dual and causal representation of scattering amplitudes (https://bitbucket.org/wjtorresb/lotty).