Measurement of branching fraction ratios and $\mathrm{CP}$ asymmetries in $B^{\pm }\to D_{\mathrm{CP}}{K}^{\pm }$

We report results on the decay $B^{-}\to D_{\mathrm{CP}}{K}^{-}$ and its charge conjugate using a data sample of $85.4\times {10}^6$ $B\overline{B}$ pairs recorded at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ storage ring. Ratios of branching fractions of Cabibbo-suppressed to Cabibbo-favored processes are determined to be $\mathcal{B}{(B}^{-}\to D^0{K}^{-})/\mathcal{B}{(B}^{-}\to D^0{\pi }^{-})=0.077\mathrm{}\pm 0.005\left(\mathrm{stat}\right)\pm 0.006\left(\mathrm{syst}\right),$ $\mathcal{B}{(B}^{-}\to D_1{K}^{-})/\mathcal{B}{(B}^{-}\to D_1{\pi }^{-})=0.093\mathrm{}\pm 0.018\left(\mathrm{stat}\right)\pm 0.008\left(\mathrm{syst}\right)$ and $\mathcal{B}{(B}^{-}\to D_2{K}^{-})/\mathcal{B}{(B}^{-}\to D_2{\pi }^{-})=0.108\mathrm{}\pm 0.019\left(\mathrm{stat}\right)\pm 0.007\left(\mathrm{syst}\right)$ where the indices 1 and 2 represent the $CP=+1\mathrm{}$ and $CP=-1$ eigenstates of the $D^0-D^0$ system, respectively. We find the partial-rate charge asymmetries for $B^{-}\to D_{\mathrm{CP}}{K}^{-}$ to be ${\mathcal{A}}_1=0.06\mathrm{}\pm 0.19\left(\mathrm{stat}\right)\pm 0.04\left(\mathrm{syst}\right)$ and ${\mathcal{A}}_2=-0.19\pm 0.17\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right).\mathrm{}$