Evidence for the Suppressed Decay $B^{-}\to D{K}^{-}$, $D\to K^{+}{\pi }^{-}$

The suppressed decay chain $B^{-}\to D{K}^{-}$, $D\to K^{+}{\pi }^{-}$, where $D$ indicates a ${\overline{D}}^0$ or $D^0$ state, provides important information on the $CP$-violating angle ${\varphi }_3$. We measure the ratio ${\mathcal{R}}_{DK}$ of the decay rates to the favored mode $B^{-}\to D{K}^{-}$, $D\to K^{-}{\pi }^{+}$ to be ${\mathcal{R}}_{DK}=[{1.63}_{-0.41}^{+0.44}(\mathrm{stat}{)}_{-0.13}^{+0.07}(\mathrm{syst})]\times {10}^{-2}$, which indicates the first evidence of the signal with a significance of $4.1\sigma$. We also measure the asymmetry ${\mathcal{A}}_{DK}$ between the charge-conjugate decays to be ${\mathcal{A}}_{DK}=-{0.39}_{-0.28}^{+0.26}(\mathrm{stat}{)}_{-0.03}^{+0.04}(\mathrm{syst})$. The results are based on the full $772\times {10}^6$ $B\overline{B}$ pair data sample collected at the ${\rm Y}(4S)$ resonance with the Belle detector.

Figure 1

$\Delta E$ ($NB>0.9$) and $NB$ ($|\Delta E|<0.03\mathrm{GeV}$) distributions for $[K^{+}{\pi }^{-}{]}_D{K}^{-}$ (left) and $[K^{+}{\pi }^{-}{]}_D{\pi }^{-}$ (right). Charge-conjugate decays are included. In these plots, $[K^{+}{\pi }^{-}{]}_D{K}^{-}$ components are shown by thicker dashed curves (red), and $[K^{+}{\pi }^{-}{]}_D{\pi }^{-}$ components are shown by thinner dashed curves (magenta). $B\overline{B}$ backgrounds are shown by dash-dotted curves (green) while $q\overline{q}$ backgrounds are shown by dotted curves (blue). The sums of all components are shown by solid curves (black).

Figure 2

$\Delta E$ distributions ($NB>0.9$) for $[K^{+}{\pi }^{-}{]}_D{K}^{-}$ (left upper), $[K^{-}{\pi }^{+}{]}_D{K}^{+}$ (right upper), $[K^{+}{\pi }^{-}{]}_D{\pi }^{-}$ (left lower), and $[K^{-}{\pi }^{+}{]}_D{\pi }^{+}$ (right lower). The curves show the same components as in Fig. 1.