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

Abstract

The Standard Model (SM) predicts that $\Delta A_{\mathrm{CP}}$, 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 $\Delta A_{\mathrm{CP}}$ 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, $\Delta A_{\mathrm{CP}}$ 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.

Comments: 31 pages, 7 captioned figures. Analysis modified from v1. Accepted for publication in Physical Review D