Feynman integrals exhibit beautiful and sometimes unexpectedly interesting mathematical structure.
Feynman integrals exhibit beautiful and sometimes unexpectedly interesting mathematical structure.
Theoretical predictions, derived from perturbative calculations based on the Standard Model, are fundamental to interpreting the data provided by the Large Hadron Collider (LHC). Scattering amplitudes serve as the building blocks for these predictions. My research focuses on the computation of higher-order contributions to scattering amplitudes in perturbative quantum field theory (QFT), specifically within the frameworks of quantum chromodynamics (QCD) and electroweak (EW) theory.
A significant part of my work involves calculating next-to-next-to-leading order (NNLO) corrections in the perturbative series expansion of coupling constants for scattering amplitudes, represented as multi-loop Feynman diagrams. These computations are particularly challenging, especially for processes involving multiple kinematic scales or massive particles in the loop. In such scenarios, the function space of the analytic results for scattering processes becomes increasingly complicated. Advancing the NNLO multi-scale frontier requires a deep understanding of the function space of contributing Feynman integrals, as well as the development of novel techniques to manage their complexity.
Beyond the phenomenological applications, I am deeply interested in the mathematical properties of Feynman integrals. For instance, in processes with massless internal propagators, the analytic results of Feynman integrals are often expressed using multiple polylogarithms (MPLs). While analytic solutions for single-scale polylogarithmic cases are largely automated, no general algorithms exist for multi-scale scenarios.
When massive internal propagators are introduced, the complexity increases, often extending beyond the realm of MPLs to involve integrals defined on elliptic curves. Finding analytic results in such cases is even more challenging. With additional scales or loops, the function space can expand further, traversing beyond elliptic curves to involve K3 surfaces and higher-order Calabi–Yau manifolds. Recent findings highlight that elliptic integrals are not only significant for scattering amplitudes in QFT and string theory but also play a crucial role in gravity. This underscores the need for a deeper understanding of Feynman integrals associated with these advanced mathematical structures