Utilising $B \to \pi K$ Decays at the High-Precision Frontier

Abstract

$B \to \pi K$ decays have received a lot of attention over the last two decades, with puzzling patterns in the previous data. They form a particularly interesting set of decays as they are dominated by QCD penguin topologies. Electroweak penguin amplitudes also play a significant role, giving a contribution at the level of the tree topologies. We find a discrepancy in the correlation between the CP asymmetries of $B^0_d \to \pi^0 K_{\rm S}$. A modified electroweak penguin sector offers an attractive avenue for new particles to enter. We provide a new method to determine the electroweak penguin parameters, and apply it to current data for charged $B \to \pi K$ decays. It uses an isospin relation and requires only $SU(3)$ input to fix a normalization. A central role is played by the mixing-induced CP asymmetry of $B^0_d\to\pi^0K_{\rm S}$. The implementation of our strategy in the high-precision era of $B$-physics has the exciting potential to establish New Physics in the electroweak penguin sector.