SMEFT & HEFT: hunting for new physics footprints at the LHC

Over a decade after the Higgs discovery, the hunt for physics beyond the Standard Model faces the possibility that new particles might be too heavy to be seen at the LHC. In such a scenario, they would only leave small non-resonant traces in the measured distributions, that are described by an Effective Field Theory (EFT). Specifically, at LHC energies, these signatures are captured by the so-called SM-EFT and Higgs-EFT. 
After a pedagogical introduction to the formalism of these two theories, the talk will first review the enormous theoretical and experimental progress made in the past decade towards implementing "agnostic" interpretations of experimental data, discussing also current limitations and future prospects. 
In a second part, the talk will present some recent progress in the long-standing quest of disentangling SM-EFT from Higgs-EFT at a formal level, adopting a geometric description of the scalar sector. The discussion will be based on 2308.00017, where we introduce particular structures called jet bundles to capture higher-derivative terms in the EFT expansion.