Lotty -- The loop-tree duality automation

TL;DR

The paper introduces Lotty, a Mathematica package that automates the loop-tree duality at multi-loop levels, enabling the representation of multi-loop amplitudes in a physical, causal form and demonstrating its numerical stability.

Contribution

Lotty automates the loop-tree duality at multi-loop levels, facilitating causal representation of multi-loop Feynman integrands and supporting all-loop conjectures.

Findings

Lotty successfully automates multi-loop amplitude representations.

Numerical stability is confirmed for two-loop topologies.

Supports the all-loop causal representation conjecture.

Abstract

Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the representation of any multi-loop amplitude can be brought in a form, at integrand level, that only displays physical information, which we refer to as the causal representation of multi-loop Feynman integrands. In order to elucidate the role of Lotty in this automation, we recall results obtained for the calculation of the dual representation of integrands up-to four loops. Likewise, within Lotty framework, we provide support to the all-loop causal representation recently conjectured by the same author. The numerical stability of the integrands generated by Lotty is studied in two-loop planar and non-planar topologies, where a numerical integration is performed and compared with known results.