Flavor symmetries in the SMEFT: theory and phenomenology

.The Standard Model Effective Field Theory provides a powerful and systematic framework for studying physics beyond the Standard Model by incorporating higher-dimensional operators that respect symmetries. Within SMEFT, the flavor structure of these operators plays a crucial role in understanding fundamental aspects such as fermion masses, mixing, and possible new sources of flavor violation. In this thesis, we analyze how the imposition of specific flavor symmetries, namely U(3)^5 and U (2)^5 flavor symmetries, constrain the SMEFT operators number and affect the flavor dynamics of the theory. The U (3)5 symmetry, which corresponds to treating the three generations of fermions as indistinguishable at leading order, serves as a useful baseline for minimal flavor violation. On the other hand, the U(2)^5 distinguishes the third generation from the first two, providing a framework that is well-motivated by the hierarchical structure observed in fermion masses and mixing. The breaking patterns of these symmetries provide a rationale for the classification of new physics contributions to flavor observables. A crucial aspect of our analysis involves renormalization group evolution , which governs the scale dependence of the SMEFT operators. The implementation of flavor symmetries in the SMEFT typically implies a truncation of the operator series in powers of the symmetry-breaking parameters. Therefore, to determine the RG evolution of the Wilson coefficients, it is necessary to derive RGEs that are truncated consistently at the chosen order in the symmetry-breaking insertions. To facilitate this, we introduce the "RunSMEFT" code. The phenomenological implications of these flavor symmetries are then examined in a few experimental scenarios, with a particular focus on top physics. The top quark sector serves as a crucial testing ground for new physics effects.