Phenomenological aspects of the Standard Model Effective Field Theory in Higgs physics

The Standard Model of Particle Physics has been confirmed experimentally with extraordinary precision, most notably with the prediction and the 2012 discovery of the Higgs boson. Despite this success, various phenomena suggest the need for extending the Standard Model, although no clear experimental evidence has yet pointed to the correct direction. Many key properties of the Higgs boson remain largely unexplored, motivating further experimental and theoretical research. Understanding these aspects could provide crucial insights into unresolved issues in the Standard Model and guide the search for new physics. The absence of significant deviations from Standard Model predictions suggests a substantial mass gap between the known particles and any new particles, making effective field theories an ideal approach for parameterizing potential effects from unknown physics. Among these, the Standard Model effective field theory has become one of the most widely used frameworks, and it forms the foundation of this work. Accurately probing small deviations from the Standard Model requires higher-order loop calculations, which refine precision predictions but also introduce significant technical challenges. The first part of this thesis focuses on addressing one such challenge: the treatment of $\gamma_5$ in dimensional regularization. This analysis is performed in the context of two-loop contributions from effective four-top quark operators in single-Higgs boson production via gluon fusion, performing the computation within two schemes to continuate $\gamma_5$ to non-integer dimensions, namely NDR and BMHV. We propose a strategy for obtaining physical results that are independent of the chosen scheme, ensuring consistency and meaningful predictions across different computational approaches. This is achieved by examining the interplay between different operators at the loop level. The significance of these findings is demonstrated through a fit to Higgs boson data, highlighting the subtleties of the issue and summarizing the key results. A further aspect of loop calculations is the energy-scale dependence of the theory's parameters, introduced through the renormalization process. With the increasing precision of experimental measurements, these effects, known as running effects, become increasingly important, especially in scenarios with widely separated energy scales. The second part of this thesis is devoted to an in-depth study of these renormalization group effects and their impact on single and double Higgs boson production channels at LHC.