Multi-Scale Amplitudes For Collider Physics

The large amount of data that will be collected by experiments at the Large Hadron Collider in the coming years will lead to an unprecedented increase in the precision of their measurements. To benefit from these precise measurements and improve our understanding of the fundamental laws of physics, we must obtain a broad set of theoretical predictions to corresponding levels of precision. Crucially, these predictions require the computation of multi-particle multi-scale two-loop scattering amplitudes involving massive particles. This poses a formidable challenge that we are currently unable to meet.In recent years, a new framework for the calculation of amplitudes has begun to emerge. Building on a deep understanding of the physical and mathematical properties of the amplitudes, it uses numerical evaluations to constrain an Ansatz for the analytic form of the amplitude.Working in this framework, MultiScaleAmp will redefine the state of the art in multi-scale two-loop amplitude calculation by singling out the main bottlenecks in current approaches. In particular, it will make use of geometric and mathematical tools to understand the analytic structures which underpin the amplitudes, and introduce techniques which can handle a number of scales beyond the reach of current approaches. This will lead to a wide set of two-loop amplitude calculations, triggering a new era of theoretical precision.In summary, MultiScaleAmp will make revolutionary conceptual developments in multi-scale amplitude computations, and usher in a new era of precision at hadron colliders. It will deliver:1. Novel approaches for the computation of multi-scale Feynman integrals.2. New techniques for the computation of two-loop amplitudes with many scales.3. The necessary two-loop amplitudes for the production at hadron colliders of jets in associationwith heavy particles such as Higgs bosons, top quarks or vectors bosons.