Feynman Integrals for Phenomenology

Objective

Providing precision predictions for leptonic processes has become an urgent challenge in particle physics. Low-energy experiments and future colliders such as the FCC-ee demand corrections at next-to-next-to-leading and higher orders in Quantum Electrodynamics and Electroweak Theory, where multi-loop Feynman integrals play a central role. The presence of several mass scales makes these integrals exceptionally difficult, yet exact mass dependence is required to regulate collinear singularities and to achieve the accuracy needed to test the Standard Model at the percent level. Existing approaches, whether purely numerical or analytic, face severe limitations for such multi-scale integrals, creating a critical gap between theoretical methods and experimental needs. This project extends a recently developed framework to close this gap by exploiting the hidden geometric structure of Feynman integrals. I will implement automated tools that solve the differential equations governing the integrals, enabling efficient multivariate series expansions. These developments will then be applied to multi-loop integrals with full mass dependence, opening the way to precision predictions for processes central to current and future experiments. The project produces tools to address integrals currently intractable with numerical methods, applying them to processes of direct phenomenological relevance. The resulting computations will feed into existing prediction frameworks, ensuring that formal advances translate into practical improvements for precision tools. By merging progress in Feynman integral theory with collider phenomenology, the project demonstrates the power of interdisciplinary approaches to accelerate theoretical advances and meet current experimental demands.