Asymptotic expansions and causal representations through the loop-tree duality

Abstract

Large-scale particle physics experiments have provided a vast amount of high- quality data during the last decades. A leading role has been played by the Large Hadron Collider where the evaluation and analysis of its second run is currently still in progress while the third run is about to start, promising ever higher pre- cision data of particle collisions and subsequent decays. The agreement between experimental observations and theoretical predictions using the Standard Model of Particle Physics is excellent. Indeed, this is a problem since there are cur- rently few clues for how genuine shortcomings of the model can be overcome. New physics phenomena can appear either at higher energies, which would re- quire the construction of an even larger particle collider, or as small deviations accessible only through precision calculations. These involve higher-order quan- tum corrections which pose technical challenges. An alternative to the traditional method has been proposed in the form of the loop-tree duality theorem. In this work a newly found purely causal representation of the dual integrands and the definitions of several classes of multiloop topologies as well as their loop-tree du- ality representations are presented. The main part of this work is focused on the development of a framework for using asymptotic expansions in the context of the loop-tree duality. Previously found expansions in the leading order Higgs boson decay are analyzed and a general method is derived for defining asymptotic expansion of scattering amplitudes within the loop-tree duality formalism. This method is applied and analyzed for the scalar two- and three-point functions at one-loop order and applied to highly boosted Higgs boson production.