The decays B 0 d → J/ψK 0 S and B 0 s → J/ψφ play a key role for the determination of the B 0 q -B 0 q (q = d, s) mixing phases φ d and φ s , respectively. The theoretical precision of the extraction of these quantities is limited by doubly Cabibbo-suppressed penguin topologies, which can be included through control channels by means of the SU(3) flavour symmetry of strong interactions. Using the currently available data and a new simultaneous analysis, we discuss the state-of-the-art picture of these effects and include them in the extracted φ q values. We have a critical look at the standard model predictions of these phases and explore the room left for new physics. Considering future scenarios for the high-precision era of flavour physics, we illustrate that we may obtain signals for physics beyond the standard model with a significance well above five standard deviations. We also determine effective colour-suppression factors of B 0 d → J/ψK 0 , B 0 s → J/ψK 0 S and B 0 d → J/ψπ 0 decays, which serve as benchmarks for QCD calculations of the underlying decay dynamics, and present a new method using information from semileptonic B 0 d → π − + ν and B 0 s → K − + ν decays.
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