Asymptotic expansions through the loop-tree duality

Abstract

First results towards a general method for asymptotic expansions of Feynman amplitudes in the loop-tree duality (LTD) formalism are presented. The asymptotic expansion takes place at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. Additionally, the UV behaviour of the individual contributions to the asymptotic expansion emerges only in the first terms of the expansion and is renormalized locally in four space-time dimensions. These two properties represent an advantage over the method of Expansion by Regions (EbR). We explore different approaches in different kinematical limits, and derive general guidelines with several benchmark examples.

23 pages, 7 figures

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• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Loop Feynman integration on a quantum computer
• Expansion by regions with pySecDec