Abstract
Asymptotic expansions of Feynman amplitudes in the loop-tree duality formalism are implemented at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. The ultraviolet 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. We explore different approaches in different kinematical limits, and derive explicit asymptotic expressions for several benchmark configurations.
Highlights
The interest in asymptotic expansions within perturbative Quantum Field Theory (pQFT) arises from their potential to facilitate analytic results in specific kinematic configurations, when full analytic calculations in Dimensional Regularization (DREG) are not possible
The interest in asymptotic expansions within pQFT arises from their potential to facilitate analytic results in specific kinematic configurations, when full analytic calculations in DREG are not possible
As an example for a new-physics scenario likely to benefit from asymptotic expansions highly-boosted Higgs boson production may be mentioned: while the regime of small transverse momentum has been calculated with a point-like interaction encoding the top-quark loop [6,7], first attempts at the full calculation necessary for obtaining the large transverse momentum distribution have been published recently and rely on either numerical integration [8] or expansions in the Integration by Parts identities [9]
Summary
The interest in asymptotic expansions within pQFT arises from their potential to facilitate analytic results in specific kinematic configurations, when full analytic calculations in DREG are not possible. This feature allowed the development of the Four-dimensional Unsubtraction method (FDU) [38,39,40] It leads to an additional characteristic: in comparison to the original Feynman amplitude as a function of Minkowski four-momenta the size of scalar products appearing in the dual integrand can be directly compared to external scales. This allows the development of a well-defined formalism of asymptotic expansions of the integrand.
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