Inside the Precision Era: Exploring New Physics through Quark Flavor Transitions at LHCb

The Standard Model (SM) of Particle Physics is a quantum field theory that describes elementary particles and their interactions. While experiments have repeatedly confirmed its predictions, the SM cannot explain several phenomena such as dark matter or the matter-antimatter misbalance present in the observed Universe. Therefore, new physics (NP) models are needed. This thesis explores these issues in three different approaches. First, to test the SM, the most accurate measurement of the CP violating phase $\phi^{c\bar{c}s}_s$ is achieved by the analysis of $B_s^0 \rightarrow J/\psi K^+K^-$ decays collected by the LHCb detector during the data-taking years 2015-2018. The complex phase $\phi^{c\bar{c}s}_s$ is directly related to the complex phase present in the parametrization of the CKM matrix and therefore responsible for the CP violation within the SM in the quark sector. The CP violation present in the CKM matrix is not enough to explain the matter-antimatter imbalance and hence, is a perfect place for looking for NP footprints. This analysis is categorized as a golden channel as it also constitutes the world's best measurement of the decay width of the $B_s^0$ meson, the difference between decay widths of the mass eigenstates of the $B_s^0$ meson and the CP violating parameter $|\lambda|$, which is related with the CP violation present in the decay. Second, to improve future measurements of CP violation in the interference between the decay and the decay through mixing, advancements in the flavor tagging algorithm technique using the inclusive approach are analyzed. This experimental technique is used to infer through the information present in the tracks of the event the flavor of the $B$ meson at the production point. For this, a DeepSet classifier is implemented and relative improvements to the classical techniques of 22% and 37% in $B_s^0 \rightarrow D_s^-\pi^+$ and $B^0\rightarrow J/\psi K^*$, respectively are observed. Finally, the implications of the measurement of $\phi^{c\bar{c}s}_s$ as well as other flavor precision observables in the context of supersymmetric models, which address some of the limitations of the SM, such as providing a valid DM candidate are reported in this thesis.