The Beauty of Flavour Physics

This thesis discusses benchmark decays of $B$ mesons, which are excellent tools for testing the theory of the Standard Model of particle physics and exploring New Physics effects. A central part of our analysis is the exploration of the violation of the CP symmetry, where C stands for charge conjugation and P for parity (i.e., space inversion). Since CP violation has different manifestations, we explore the topic by categorizing the decays according to their dynamics and study each category separately. The first category refers to decays dominated by tree topologies, although penguin (loop) topologies also play a role. Key examples include the $B^0_d \to J/\psi K^0_S$ and $B^0_s \to J/\psi \phi$ modes. These decays are central for exploring parameters associated with the phenomenon of $B^0_q$-$\bar{B}^0_q$ mixing. We have suggested methods for properly including the penguin contributions in the analysis of these mixing parameters. There are also decays which are pure tree transitions, such as the $B_s \to D_s^{\pm} K^{\mp}$ system and the related modes. These decays allow theoretically clean determinations of the angle $\gamma$ of the Unitarity Triangle. Utilising experimental data, we have revealed puzzling patterns in these decays which could be footprints of New Physics. We have presented a model-independent analysis to account for such New Physics effects. Another category includes decays dominated by penguins, such as the $B \to \pi K$ channels. We have addressed the long-standing puzzling patterns in the data within this system, discussing correlations between key observables. We have proposed strategies for further exploring these intriguing cases and optimally determining the parameters describing the puzzling effects. These strategies can be applied in the future high-precision experiments in $B$ physics. Last but not least, there are decays arising from electroweak penguins and box topologies, such as the leptonic $B^{0}_{(s)} \to \mu^{+} \mu^{-}$ modes, which also have a rich phenomenology related to CP violation. These are very rare processes in the Standard Model. In our analysis, we have utilised these interesting modes as a probe for New Physics. Throughout this thesis, we have discussed exciting new perspectives to further explore CP violation. Comparing our theoretical predictions with experimental measurements allows us to test the Standard Model quark sector and search for physics beyond the Standard Model, highlighting the importance of synergies between theorists and experimentalists. Thrilling times lie ahead of us as we move into the era of the highest precision in $B$ physics. Utilising our theoretical analyses and methods we may eventually identify New Physics and reveal new sources of CP violation, opening up new horizons in the field of particle physics.