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.

arXiv comment23 pages, 7 figures

References in corpus (25)

• Asymptotic expansion of Feynman integrals near threshold
• Higgs boson production in association with a jet at next-to-next-to-leading order
• Precise QCD predictions for the production of Higgs+jet final states
• Expansion by regions: revealing potential and Glauber regions automatically
• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Geometric approach to asymptotic expansion of Feynman integrals
• Foundation and generalization of the expansion by regions
• NLO QCD corrections to Higgs boson plus jet production with full top-quark mass dependence
• From loops to trees by-passing Feynman's theorem
• Loop Tree Duality for multi-loop numerical integration
• Four-dimensional unsubtraction with massive particles
• Towards gauge theories in four dimensions
• A Tree-Loop Duality Relation at Two Loops and Beyond
• Four-dimensional unsubtraction from the loop-tree duality
• Higgs bosons with large transverse momentum at the LHC
• Open loop amplitudes and causality to all orders and powers from the loop-tree duality
• On the singular behaviour of scattering amplitudes in quantum field theory
• Universal four-dimensional representation of $H\to \gamma \gamma$ at two loops through the Loop-Tree Duality
• Numerical Loop-Tree Duality: contour deformation and subtraction
• On the status of expansion by regions
• Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry
• Causality and Unitarity via the Tree-Loop Duality Relation
• High-Energy Expansion of Two-Loop Massive Four-Point Diagrams
• Universal dual amplitudes and asymptotic expansions for $gg\to H$ and $H\to \gamma \gamma$ in four dimensions
• On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators

Cited by in corpus (7)

• Geometrical approach to causality in multi-loop amplitudes
• Quantum algorithm for Feynman loop integrals
• Projected transverse momentum resummation in top-antitop pair production at LHC
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Loop Feynman integration on a quantum computer
• Expansion by regions with pySecDec