Searching for penguin footprints: Towards high precision CP violation measurements in the B meson systems

In the quark-flavour sector of the Standard Model (SM), measurements of CP violation in the $B^0_d\to J/\psi K_{\rm S}^0$ and $B^0_s\to J/\psi \phi$ decays play key roles in the search for signs of beyond the SM physics. For these observables, large deviations from the SM expectation have now been ruled out, but the quest for new physics still continues as the forthcoming physics runs at the LHC and KEKB super B-factory promise to reduce the experimental uncertainties even further. These prospects make it mandatory to improve the theoretical interpretation of the measurements, which is limited by uncertainties from doubly Cabibbo-suppressed penguin topologies. To get a handle on these penguin contributions, which cannot be calculated reliably in QCD, we explore a strategy that relies on the $SU(3)$ flavour symmetry of QCD and data from decays with similar dynamics. The research reported in this thesis is a shared project between theoretical and experimental particle physics. On the theoretical side, we explore the potential of the $SU(3)$ symmetry based method and analyse the currently available information on the penguin contributions. In the case of the $B^0_s\to J/\psi \phi$ mode, used to determine the $B^0_s$$-$$\bar B^0_s$ mixing phase $\phi_s$, the penguin effects can be controlled through $B^0_d\to J/\psi \rho^0$ and $B^0_s\to J/\psi \bar{K}^{*0}$ decays. For the measurement of $\sin2\beta$ from $B^0_d\to J/\psi K_{\rm S}^0$, the $U$-spin-related decay $B^0_s\to J/\psi K_{\rm S}^0$ offers a powerful tool to control the penguin effects. The experimental half of the research focuses on the measurement of the decay channel $B^0_s\to J/\psi K_{\rm S}^0$, using data corresponding to an integrated luminosity of 3.0 fb$^{-1}$ of proton--proton collisions recorded with the LHCb detector at centre-of-mass energies of 7 and 8 TeV. It focusses on a first measurement of decay-time-dependent CP asymmetries in the decay $B^0_s\to J/\psi K_{\rm S}^0$, and a measurement of the ratio of branching fractions $\mathcal{B}(B^0_s\to J/\psi K_{\rm S}^0)/\mathcal{B}(B^0_d\to J/\psi K_{\rm S}^0)$