Exploring [Formula: see text] decays at the high-precision frontier

The [Formula: see text] system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic [Formula: see text] parameters from data where new measurements of direct CP violation in [Formula: see text] resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the [Formula: see text] parameters can be converted into their [Formula: see text] counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is [Formula: see text] 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 [Formula: see text] , which are the theoretically cleanest [Formula: see text] probes. Interestingly, they show tensions with respect to the Standard Model. Should this [Formula: see text] 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 [Formula: see text] dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.