Complete analysis of all $B\to \pi K$ decays

The Standard Model (SM) predicts that $\Delta A_{\rm CP}$, the difference between the direct CP asymmetries for the modes $B^+\to \pi^0 K^+$ and $B^0\to \pi^- K^+$ that are related by weak isospin, should be close to zero. There has been a recent claim by the LHCb Collaboration that the measured value of $\Delta A_{\rm CP}$ shows an uncomfortable tension with the SM prediction, almost at the $8\sigma$ level. Motivated by this claim, we critically re-examine the data on all the $B\to \pi K$ modes, including the CP asymmetries and CP-averaged branching fractions. From a combined Bayesian analysis with the topological amplitudes and their phases as the free parameters, we find that the best-fit region has a large overlap with the parameter space favoured in the SM, albeit with some enhancement for the electroweak penguin and the colour-suppressed tree amplitudes, consistent with the findings of earlier studies. We find that in this SM-like region, $\Delta A_{\rm CP}$ is more than 5$\sigma$ away from zero and the tension with the global average, as well as the LHCb result, is within $2\sigma$. Thus we conclude that there is not yet enough motivation to go beyond the SM.