New methods for evaluating one-loop corrections of multi-jet production at the Large Hadron Collider

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The Large Hadron Collider aims to explore electroweak symmetry breaking and search for new physics at Tera electron Volt energy scales. To analyze the vast data generated, precise predictions for processes within the Standard Model and its extensions are essential. Perturbation theory, which expands hard scattering matrix elements in quantum field coupling constants, is a key tool in collider physics. While tree-level diagrams are well-developed and largely automated, incorporating quantum corrections at one-loop order poses significant challenges, especially for high multiplicity processes. This difficulty arises from the sheer number of Feynman diagrams and the complex integration over virtual degrees of freedom required for each diagram. This book presents alternative methods based on unitarity and integrand reduction for calculating one-loop amplitudes in massless Quantum Chromodynamics (QCD). The approach constructs the entire one-loop integrand from products of on-shell tree-level amplitudes, allowing the full one-loop amplitude to be derived without explicitly evaluating individual diagrams. The algorithm is thoroughly examined for numerical accuracy and runtime performance. As a proof of concept, the methods are applied to compute the phenomenologically significant process of four-jet production at the Large Hadron Collider.