Measurements of branching fractions and direct $CP$ asymmetries for $B\to K\pi$, $B\to \pi \pi$ and $B\to KK$ decays

We report measurements of the branching fractions and direct $CP$ asymmetries (${\mathcal{A}}_{CP}$) for $B\to K\pi$, $\pi \pi$ and $KK$ decays (but not ${\pi }^0{\pi }^0$) based on the final data sample of $772\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We set a 90% confidence-level upper limit for $K^{+}{K}^{-}$ at $2.0\times {10}^{-7}$; all other decays are observed with branching fractions ranging from ${10}^{-6}$ to ${10}^{-5}$. In the $B^0/{\overline{B}}^0\to K^{\pm }{\pi }^{\mp }$ mode, we confirm Belle’s previously reported large ${\mathcal{A}}_{CP}$ with a value of $-0.069\pm 0.014\pm 0.007$ and a significance of $4.4\sigma$. For all other flavor-specific modes, we find ${\mathcal{A}}_{CP}$ values consistent with zero, including ${\mathcal{A}}_{CP}(K^{+}{\pi }^0)=+0.043\pm 0.024\pm 0.007$ with $1.8\sigma$ significance. The difference of $CP$ asymmetry between $B^{\pm }\to K^{\pm }{\pi }^0$ and $B^0/{\overline{B}}^0\to K^{\pm }{\pi }^{\mp }$ is found to be $\Delta {\mathcal{A}}_{K\pi }\equiv {\mathcal{A}}_{CP}(K^{+}{\pi }^0)-{\mathcal{A}}_{CP}(K^{+}{\pi }^{-})=+0.112\pm 0.027\pm 0.007$ with $4.0\sigma$ significance. We also calculate the ratios of partial widths for the $B\to K\pi$ decays. Using our results, we test the validity of the sum rule ${\mathcal{A}}_{CP}(K^{+}{\pi }^{-})+{\mathcal{A}}_{CP}(K^0{\pi }^{+})\frac{\Gamma (K^0{\pi }^{+})}{\Gamma (K^{+}{\pi }^{-})}-{\mathcal{A}}_{CP}(K^{+}{\pi }^0)\frac{2\Gamma (K^{+}{\pi }^0)}{\Gamma (K^{+}{\pi }^{-})}-{\mathcal{A}}_{CP}(K^0{\pi }^0)\frac{2\Gamma (K^0{\pi }^0)}{\Gamma (K^{+}{\pi }^{-})}=0$ and obtain a sum of $-0.270\pm 0.132\pm 0.060$ with $1.9\sigma$ significance.

Figure 1

$\Delta E$ (left) and $M_{\mathrm{bc}}$ (right) distributions for $B^0\to K^{+}{\pi }^{-}$, $B^0\to {\pi }^{+}{\pi }^{-}$, $B^{+}\to K^{+}{\pi }^0$, $B^{+}\to {\pi }^{+}{\pi }^0$ and $B^0\to K^0{\pi }^0$ candidates. Points with error bars represent the data, while the curves denote various components of the fit: signal (solid red), continuum (dashed blue), charmless $B$ background (hatched green), background from misidentification (filled yellow), and sum of all components (solid black). The $\Delta E$ and $M_{\mathrm{bc}}$ projections of the fits are for events in the ${\mathcal{R}}^{\prime }$ signal enhanced region (${\mathcal{R}}^{\prime }>1.47$ for $K^{+}{\pi }^{-}$, ${\pi }^{+}{\pi }^{-}$, and $K^0{\pi }^0$; ${\mathcal{R}}^{\prime }>2.71$ for others) and $M_{\mathrm{bc}}>5.27\mathrm{GeV}/c^2$ or $-0.14(-0.06)\mathrm{GeV}<\Delta E<0.06\mathrm{GeV}$ with (without) a ${\pi }^0$ in the final state.

Figure 2

$\Delta E$ (left) and $M_{\mathrm{bc}}$ (right) distributions for $B^{+}\to K^0{\pi }^{+}$, $B^{+}\to {\overline{K}}^0{K}^{+}$, $B^0\to K^0{\overline{K}}^0$ and $B^0\to K^{+}{K}^{-}$ candidates. The selections for fit projections and PDF component descriptions are identical to those in Fig. 1 (${\mathcal{R}}^{\prime }>1.47$ for $K^0{\overline{K}}^0$; ${\mathcal{R}}^{\prime }>2.71$ for others).

Figure 3

The $M_{\mathrm{bc}}$ distributions for $B^0/{\overline{B}}^0\to K^{\pm }{\pi }^{\mp }$ (top) and $B^{\pm }\to K^{\pm }{\pi }^0$ (bottom). The selections for fit projections and PDF component descriptions are identical to those described in Fig. 1.