On the computation of loop amplitudes using the Loop-Tree Duality formalism
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
The calculation of scattering amplitudes beyond the leading order or tree level approximation in perturbation theory is required to match the increasing precision of measurements at modern particle colliders where the fundamental structure of nature is put to test. The approach to higher-order calculations, based on the expansion on Feynman diagrams, becomes increasingly cumbersome beyond the simplest 2 to 2 processes. Moreover, the scattering amplitudes at a given perturbative order receive virtual and real corrections, which are given by divergent integrals over different integration measures. Although the divergences between the sum of all the contributions cancel against each other, realizing this cancellation in an automated fashion is difficult, and a framework to unify the integration measures is desired in order to pave the way for the possibility to cancel the divergences arising in the real and virtual contributions at the integrand level. In this thesis, the Loop-Tree Duality (LTD) formalism is utilized to reduce the dimension of the virtual loop integrals to that of the real radiation corrections. The formalism is applied in first instance to single Feynman integrals, resulting in the construction of integrands which have a tree-like structure where the usual Feynman propagators acquire a modified causal prescription for the position of the poles. Using the Feynman diagram expansion of the scattering amplitudes and the decomposition of each virtual contribution into trees, an expression in terms of a tree amplitude-like object is found for the integrand of the complete scattering amplitude in an arbitrary field theory. The tree structure of the integrand is then exploited to construct recursion relations which allow to compute the integrand without making reference to individual Feynman diagrams, providing a first step into the possible automation of the numerical calculation of higher-order amplitudes.