Exploring B → ππ, πK decays at the high- precision frontier

The B -> pi pi, pi K system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic B. pp parameters from data where new measurements of direct CP violation in B0 d. p0p0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the B. pp parameters can be converted into their B. pK counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is B0 d. p0KS as it exhibits mixing-inducedCPviolation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of B0 d. p0KS, which are the theoretically cleanest B. pK probes. Interestingly, they show tensions with respect to the Standard Model. Should this B. pK puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the B. pK dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.