TOPGUN3 · TOP-pair production Gaining Unprecedented N3LO accuracy in QCD

The forthcoming High-Luminosity phase of the Large Hadron Collider (HL-LHC) will deliver percent-level precision across a wide range of observables, requiring equally accurate theoretical predictions. For several key processes, this demands next-to-next-to-next-to-leading order (N3LO) accuracy in quantum chromodynamics (QCD).TOPGUN3 focuses on top-quark pair production, the dominant source of top quarks at the LHC and the main channel for determining the top-quark mass. As the heaviest known particle, the top quark strongly affects the precision of Standard Model (SM) observables and the stability of the electroweak vacuum, yet its mass remains one of the least precisely known SM parameters due to theoretical uncertainties. Achieving N3LO accuracy is therefore essential to refine the top-quark mass determination and fully exploit the HL-LHC’s discovery potential.The project’s goal is the computation of the required three-loop amplitudes within the leading-color approximation, one of the main bottlenecks to N3LO precision. This computation goes beyond the current frontier. The presence of top quarks in both the final state and loop propagators greatly increases the complexity of the amplitudes, turning their reduction to a minimal set of Feynman integrals (FIs) with rational coefficients into a major obstacle, and gives rise to FIs involving special functions beyond multiple polylogarithms, whose evaluation is challenging.To address these challenges, I will develop a new reduction package by combining and extending cutting-edge reduction methods, such as syzygy techniques and transverse integration identities. The resulting FIs will be evaluated by employing and improving advanced methods to construct optimized differential equations and solve them through generalized series expansions.The success of this project will advance computations in perturbative quantum field theory and pave the way for tackling a broad range of phenomenologically relevant processes.