The Large Hadron Collider (LHC) represents the frontier of exploration of nature at the smallest length scales. By colliding protons at near-light speeds, it produces short-lived particles whose decay patterns are recorded in complex detectors. Comparing these data to theoretical predictions has already led to the 2012 discovery of the Higgs boson and has firmly established the Standard Model (SM) as our current best description of fundamental interactions. Yet profound questions remain: the origin of dark matter, the stability of the vacuum, and the possibility of new physics at high energy scales. Because the Higgs boson couples broadly to other heavy SM particles, its properties offer a unique window into potential new phenomena. Exploiting this opportunity requires theoretical predictions of exceptional precision.
In the coming years, the LHC will enter into an era of precision measurements. Increased collision rates will yield vastly larger datasets, reducing experimental uncertainties for many observables to the percent level or below. To fully benefit from this wealth of data, theory must keep pace: the SM predictions used to interpret measurements must reach matching levels of accuracy. At the LHC, achieving this precision hinges on perturbative quantum chromodynamics (QCD), where observables are computed order-by-order in the strong coupling. While next-to-leading order calculations already describe many processes well, percent-level precision typically requires next-to-next-to-leading order (NNLO) accuracy. The central obstacle to NNLO predictions is the need for mathematical descriptions of multi-particle scattering processes: the so-called "scattering amplitude".
These amplitudes form a key building block of precision collider phenomenology, but they present a formidable challenge. Their analytic structure is highly intricate and traditional computational techniques struggle to cope with this complexity. As a result, many amplitudes essential for interpreting Higgs, top-quark, and electroweak measurements remain out of reach. A new paradigm has emerged in recent years that promises to overcome these barriers. This approach leverages deep physical and mathematical insights into the scattering amplitudes. By combining geometric tools, differential equations and modern understanding of Feynman integrals, MultiScaleAmp is pushing forward the frontiers in two-loop amplitude computation. The central idea is to reveal and exploit the underlying geometric structures that govern these amplitudes and enable computations far beyond the reach of conventional methods. This strategy will make it possible to handle processes involving many final state particles, delivering a broad class of two-loop amplitudes required for precision studies of jets, top quarks, vector bosons and the Higgs boson.
