Studies of the DecayB±→DCPK±

We report studies of the Cabibbo-suppressed decay $B^{\pm }\to D_{CP}{K}^{\pm }$, where $D_{CP}$ denotes $CP$ eigenstates of the $D^0-\overline{D^0}$ system. The analysis is based on a $29.1\mathrm{f}{\mathrm{b}}^{\mathrm{-}\mathrm{1}}$ sample collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ storage ring. We measure ratios of branching fractions, relative to Cabibbo-favored $B^{\pm }\to D_{CP}{\pi }^{\pm }$, of $\mathcal{B}(B^{-}\to D_1{K}^{-})/\mathcal{B}(B^{-}\to D_1{\pi }^{-})=0.125\pm 0.036\pm 0.010$ and $\mathcal{B}(B^{-}\to D_2{K}^{-})/\mathcal{B}(B^{-}\to D_2{\pi }^{-})=0.119\pm 0.028\pm 0.006$; the index 1 (2) denotes the $CP=+1$ $(-1)$ eigenstate. We also extract the partial rate asymmetries for $B^{\pm }\to D_{CP}{K}^{\pm }$, finding ${\mathcal{A}}_1=0.29\pm 0.26\pm 0.05$ and ${\mathcal{A}}_2=-0.22\pm 0.24\pm 0.04$.