Spinor helicity and unitarity methods for one-loop order amplitude computation

Abstract

The growing precision of our experimental apparatus requires relevant advances in the accuracy of our theoretical cross-section computation. Implying that we need to be able to calculate multi-leg and/or multi-loop corrections to various amplitudes. The purpose of this thesis is to come to this aim and to demonstrate the affinity of the Spinor Helicity Formalism in dealing with Next-to-leading order (NLO) computations related to the QCD sector. We start by employing Helicity spinors in writing scattering amplitudes resulting in expressions with a high potential for simplifications, then introduce complex momenta to find a recursive method for building Helicity tree amplitudes and at last we used Generalized Unitarity to connect amplitudes in an order by order manner. The results were a generic one-loop formulation for Helicity amplitudes that is entirely determined through cut-coefficients along with a procedure for the extraction of box and triangle coefficients generalizable to the remaining ones. We found that cut-coefficients were built out of the product of Helicity tree amplitudes which themselves are constructed using lower-point amplitudes recursively, meaning that the NLO was ultimately linked to the kinematic 3-points of the theory and that even higher orders will necessarily employ available lower order found amplitudes. Keywords : High-energy physics, SM, QCD, Spinor Helicity Formalism, Helicity Amplitude, Complex momenta, Recursion formulae, NLO, Generalized Unitarity, On-shell cut-coefficients Extraction