Lotty -- The loop-tree duality automation

2021/03/16 by Bobadilla, William J. Torres · 4 citations
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2103.09237

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.

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• General finite two-loop amplitude integrand for photoproduction in quark annihilation
• Graph theory-based automated quantum algorithm for efficient querying of acyclic and multiloop causal configurations
• Unlocking Multi-Dimensional Integration with Quantum Adaptive Importance Sampling

Related

• Causal representation and numerical evaluation of multi-loop Feynman\n integrals
• Geometry and causality for efficient multiloop representations
• Manifestly Causal Loop-Tree Duality
• The Loop-Tree Duality: Progress Report
• Analysis of symmetries in the Causal Loop-Tree Duality representations