Fingerprinting New Physics with Effective Field Theories

Given the absence of direct evidence for new resonances beyond the Standard Model (BSM) at the Large Hadron Collider (LHC) so far, a complementary strategy to search for new physics in an indirect way is provided by the Standard Model Effective Field Theory (SMEFT). As the low-energy limit of a generic ultraviolet (UV) completion of the SM, the SMEFT provides a powerful theoretical framework to correlate deviations from the SM between different processes, offering experimental sensitivity to a plethora of SM extensions. This thesis presents a state-of-the-art SMEFT interpretation of the top, Higgs, diboson and electroweak sectors, taking into account data collected at the Large Electron-Positron Collider (LEP), the SLAC Large Detector (SLD) and the LHC. We also include the effect of the upcoming High-Luminosity LHC (HL-LHC) upgrade and demonstrate the unprecedented impact on the SMEFT parameter space of two proposed electron-positron colliders: the electron-positron Future Circular Collider (FCC-ee) and the Circular Electron Positron Collider (CEPC). We present constraints both in terms of Wilson coefficients, and couplings and masses of a wide range of UV-complete models through a newly developed automatised limit-setting procedure. We further present novel methodological advances through the development of unbinned multivariate likelihoods specialised to the SMEFT that provide maximal sensitivity to new physics using classification and regression techniques from Machine Learning. Our results provide an extensive characterisation of the SMEFT parameter space as probed both by current and future colliders, providing timely input to the upcoming European Strategy for Particle Physics Update.