B→ππ, New Physics inB→πK, and Implications for RareKandBDecays

The measured $B\to \pi \pi ,\pi K$ branching ratios (BRs) exhibit puzzling patterns. We point out that the $B\to \pi \pi$ hierarchy can be nicely accommodated in the standard model (SM) through nonfactorizable hadronic interference effects, whereas the $B\to \pi K$ system may indicate new physics (NP) in the electroweak (EW) penguin sector. Using the $B\to \pi \pi$ data and the SU(3) flavor symmetry, we fix the hadronic $B\to \pi K$ parameters and show that any currently observed feature of the $B\to \pi K$ system can be easily explained through enhanced EW penguin diagrams with a large $CP$-violating NP phase. This in turn implies in particular an enhancement of the $K_{\mathrm{L}}\to {\pi }^0\nu \overline{\nu }$ rate by 1 order of magnitude, with $\mathrm{BR}(K_{\mathrm{L}}\to {\pi }^0\nu \overline{\nu })\approx 4\mathrm{BR}(K^{+}\to {\pi }^{+}\nu \overline{\nu })$, $\mathrm{BR}(K_{\mathrm{L}}\to {\pi }^0{e}^{+}{e}^{-})=O({10}^{-10})$, and $(\sin 2\beta {)}_{\pi \nu \overline{\nu }}<0$. We address also other rare $K$ and $B$ decays and $B_d\to \varphi K_{\mathrm{S}}$.