New Methods for Evaluating One-Loop Corrections of Multi-Jet Production at the Large Hadron Collider

The primary goal of the Large Hadron Collider is to investigate the nature of electroweak symmetry breaking and the search for new physics at the energy scale of Tera electron Volt. For a successful analysis of the vast amount of data, precise predictions for the processes within the Standard Model of elementary particles and its possible extensions are crucial. One of the main tools in collider physics to make rigorous quantitative predictions is perturbation theory, an expansion of the hard scattering matrix elements in the coupling constants of the quantum fields. Traditionally, observables in perturbation theory are computed evaluating Feynman diagrams. While the available techniques for tree-level diagrams are very well developed and to a large extent automated, the inclusionof quantum corrections at one-loop order represents a severe bottleneck for processes with many particles in the final state: One the one hand, this is due to the very large number of Feynman diagrams for high multiplicity processes. On the other hand, the computation of an individual one-loop Feynman diagram on its own is a non-trivial task due to the complicated integration over the virtual degrees of freedom. In this book, alternative methods based on unitarity and integrand reduction to calculate one-loop amplitudes in massless Quantum Chromodynamics (QCD) are presented. The basic ingredient is to construct the entire one-loop integrand from products of on-shell tree-level amplitudes. With algebraic techniques at the integrand level the full one-loop amplitude can then be constructed. This approach circumvents the explicit evaluation of individual one-loop Feynman diagrams. The described algorithm is carefully investigated with respect to numerical accuracy and runtime performance. As a proof of concept for the new methods, the phenomenologically interesting process of four-jet production at the Large Hadron Collider is computed.