COMPASS · Compact Analytical Multi-Loop Multi-Leg Scattering Amplitudes in Quantum Chromodynamics from their COMplex PhAse Space Singularities (COMPASS)

The Large Hadron Collider (LHC), a multi-billion-euro facility at the European Organization for Nuclear Research (CERN), collides protons at record-breaking energies. Its goal is to test the Standard Model (SM)--the quantum field theory that best describes Nature at microscopic scales--and to search for subtle signs of new physics. In this endeavour, high-precision theoretical predictions are essential, and scattering amplitudes are at their core. To match the increasing experimental precision, multi-loop, multi-leg amplitudes are required. Yet, these are often beyond the reach of current methods.Scattering amplitude computations become extremely complicated at intermediate stages. Modern methods bypass this issue through numerical evaluations with exact but unphysical number types, such as integers modulo a prime number. Yet, final analytic results can be surprisingly compact, numerically stable, and efficient to evaluate--if only they can be identified. I will spearhead methods to obtain such compact expressions, expanding their availability for next-to-next-to-leading-order predictions in quantum chromodynamics (QCD), while containing rapidly escalating computational costs.This MSCA-PF project, COMPASS (COMplex PhAse Space Singularities), combines recent advances in Feynman integral computations and integration-by-parts reduction with an original analytic reconstruction framework. By probing the mathematical structure of scattering amplitudes--their zeros, poles, and branch cuts in complexified momentum space--I will derive compact expressions for crucial, yet unknown amplitudes involving electroweak vector bosons and QCD jets. This interdisciplinary project bridges high-energy physics, algebraic geometry, number theory, and high-performance computing, delivering advances in fundamental science, pioneering computational innovations, and providing key theoretical input for LHC phenomenology.