Analytic loop amplitudes from numerics and ansatz
The Standard Model of Particle Physics is impressively consistent with the experimental measurements at the Large Hadron Collider at CERN, Geneva. In the coming years, with increased experimental statistics, precision will rise even further, allowing a unique opportunity to uncover new physics. A necessary component of this pursuit is a set of theoretical predictions made at the per cent level for a broad range of observables. In the past decade, previously unthinkable availability of precision predictions incorporating the leading quantum corrections has been made possible by technological leaps. Nevertheless, to match the discovery potential of the LHC in the near future, further theory advances will be needed.

In my recent work, I combined geometrical insights with exact numerical techniques, to perform world-first computations of the analytic form of a plethora of five-point, two-loop scattering amplitudes in both phenomenologically relevant and formally interesting theories. In this project, I will apply this technology to a range of QCD processes, culminating in new results with immediate relevance for next-to-next-to-leading order corrections at the LHC and improved fundamental understandings of scattering amplitudes. First, I will systematically apply the approach to the computation of non-planar five-parton amplitudes in QCD. Second, I will calculate the non-planar master integrals relevant for all two-loop five-point processes with one massive leg, for example the production of a Higgs boson with two jets. Then, I will break current complexity thresholds by computing the phenomenologically relevant scattering amplitudes for the production of a W, Z, or Higgs boson, each with two associated jets.

To achieve these lofty goals, I will draw on insights into the mathematical and physical structures underlying scattering amplitudes and employ modern tools such as finite-field arithmetic, analyticity-inspired techniques and computational algebraic geometry.