Despite many theoretical and experimental indications pointing to the existence of new physics, the lack of direct evidence suggests the presence of a mass gap. Effective Field Theories (EFT) provide the optimal theoretical framework to describe the possible effects of such new physics. However, the great diversity of ultraviolet (UV) models and the complexity of UV-to-EFT matching computations difficult the connection between EFT analyses and their interpretation in terms of precise models. Recent advancements in the path-integral formulation of EFT matching (and running) provide a promising approach to overcoming this issue. In this seminar, I will review the state-of-the-art path-integral techniques and present promising theoretical and computational results building on these techniques.
