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 inclusion of 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.
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