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

The B→ ππ, πK system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic B→ ππ parameters from data where new measurements of direct CP violation in Bd0→π0π0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the B→ ππ parameters can be converted into their B→ πK counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is Bd0→π0KS as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of Bd0→π0KS, which are the theoretically cleanest B→ πK probes. Interestingly, they show tensions with respect to the Standard Model. Should this B→ πK 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→ πK dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.