Drell–Yan Phenomenology in the SMEFT and Statistical Validation of Machine Learning Generators

The Standard Model of particle physics encodes our current knowledge of fundamental particles and their interactions. Although it successfully describes a wide range of experimental observations, it fails to address several open questions, such as the matter–antimatter asymmetry, the origin of neutrino masses, and the nature of dark matter. Moreover, it presents a conceptual issue in the naturalness problem, which implies an extreme fine-tuning of parameters to justify theoretically the measured value of the Higgs boson mass. The prevailing view within the particle physics community is that the Standard Model should be extended by new, heavy degrees of freedom that lie beyond the current experimental reach and that could provide answers to these open questions. The current lack of direct observations of new particles implies that the best approach to explore physics at high energy scales is through an indirect search. The Standard Model Effective Field Theory (SMEFT) offers a model agnostic framework for such searches, and has therefore attracted interest within the High Energy Physics community. In part~\ref{part:1} of this thesis, we employ the SMEFT framework to investigate possible New Physics scenarios through the study of the Drell-Yan process in the context of the LHC. We analyze a wide range of operators, including both leading and suppressed contributions, using different observables and binning strategies. In part~\ref{part:2}, we discuss the impact of Machine Learning techniques on particle physics simulations, explaining why these approaches will become necessary to respect the precision requirements posed by experimental improvements, particularly with the advent of the High-Luminosity LHC. Our work focuses on the validation of data provided by Machine Learning-based generative models, with the goal of developing robust statistical procedures to assess their reliability and to compare different models.