Evidence for Direct $CP$ Violation in $B^{\pm }\to \eta h^{\pm }$ and Observation of $B^0\to \eta K^0$

We report measurements of the branching fractions and $CP$ asymmetries for $B^{\pm }\to \eta h^{\pm }$ ($h=K$ or $\pi$) and the observation of the decay $B^0\to \eta K^0$ from the final data sample of $772\times {10}^{6}B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The measured branching fractions are $\mathcal{B}(B^{\pm }\to \eta K^{\pm })=(2.12\pm 0.23\pm 0.11)\times {10}^{-6}$, $\mathcal{B}(B^{\pm }\to \eta {\pi }^{\pm })=(4.07\pm 0.26\pm 0.21)\times {10}^{-6}$, and $\mathcal{B}(B^0\to \eta K^0)=({1.27}_{-0.29}^{+0.33}\pm 0.08)\times {10}^{-6}$, where the last decay is observed for the first time with a significance of 5.4 standard deviations ($\sigma$). We also find evidence for $CP$ violation in the charged $B$ modes, $A_{CP}(B^{\pm }\to \eta K^{\pm })=-0.38\pm 0.11\pm 0.01$ and $A_{CP}(B^{\pm }\to \eta {\pi }^{\pm })=-0.19\pm 0.06\pm 0.01$ with significances of $3.8\sigma$ and $3.0\sigma$, respectively. For all measurements, the first and second uncertainties are statistical and systematic, respectively.

Figure 1

(a) $b\to u$ tree diagram for $B^{+}\to {\eta }^{(\prime )}{K}^{+}$. (b) color-suppressed $b\to u$ tree diagram for $B^0\to {\eta }^{(\prime )}{K}^0$. (c),(d) $b\to s$ gluonic penguin diagrams for $B\to {\eta }^{(\prime )}K$.

Figure 2

$\Delta E$ (left), $M_{\mathrm{bc}}$ (middle), and ${\mathcal{R}}^{\prime }$ (right) distributions for $B^0\to \eta K^0$ candidate events with the ${\eta }_{\gamma \gamma }$ and ${\eta }_{3\pi }$ modes combined. Points with error bars represent the data, the total fit functions are shown by black solid curves, signals are shown by red solid curves, dashed blue curves show the continuum contributions, and filled green histograms are the contributions from charmless $B$ backgrounds. The $\Delta E$, $M_{\mathrm{bc}}$, and ${\mathcal{R}}^{\prime }$ projections of the fit are for candidate events that have $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.30\mathrm{GeV}/c^2$ and ${\mathcal{R}}^{\prime }>0.55$, $-0.10\mathrm{GeV}<\Delta E<0.08\mathrm{GeV}$ and ${\mathcal{R}}^{\prime }>0.55$, and $-0.10\mathrm{GeV}<\Delta E<0.08\mathrm{GeV}$ and $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.30\mathrm{GeV}/c^2$, respectively.

Figure 3

$\Delta E$ and $M_{\mathrm{bc}}$ projections for $B^{+}\to \eta h^{+}$ (left) and $B^{-}\to \eta h^{-}$ (right) candidate events with the ${\eta }_{\gamma \gamma }$ and ${\eta }_{3\pi }$ modes combined. Points with error bars represent the data, the total fit functions are shown by black solid curves, signals are shown by red solid curves, dashed curves are the continuum contributions, dotted curves are the cross-feed backgrounds from misidentification, and filled histograms are the contributions from charmless $B$ backgrounds. The $\Delta E$ and $M_{\mathrm{bc}}$ projections of the fits are for events that have $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.30\mathrm{GeV}/c^2$ and ${\mathcal{R}}^{\prime }>1.95$, $-0.10\mathrm{GeV}<\Delta E<0.08\mathrm{GeV}$, and ${\mathcal{R}}^{\prime }>1.95$, respectively.