Measurement of branching-fraction ratios and $CP$ asymmetries in $B^{\pm }\to D_{CP\pm }{K}^{\pm }$ decays at Belle and Belle II

Abstract

We report results from a study of $B^{\pm }\to D{K}^{\pm }$ decays followed by $D$ decaying to $CP$~eigenstates, where $D$ indicates a $D^0$ or ${\bar{D}}^0$ meson. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle $\ddot{I}{•}_3$. The results are based on a combined analysis of the final data set of $772\times 10^{6}B\bar{B}$ pairs collected by the Belle experiment and a data set of $198\times 10^{6}B\bar{B}$ pairs collected by the Belle~II experiment, both in electron-positron collisions at the $\hat{I}\yen (4S)$ resonance. We measure the $CP$ asymmetries to be ${\mathcal{A}}_{CP+}=(+12.5\pm 5.8\pm 1.4)\%$ and ${\mathcal{A}}_{CP-}=(-16.7\pm 5.7\pm 0.6)\%$, and the ratios of branching fractions to be ${\mathcal{R}}_{CP+}=1.164\pm 0.081\pm 0.036$ and ${\mathcal{R}}_{CP-}=1.151\pm 0.074\pm 0.019$. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries ${\mathcal{A}}_{CP+}$ and ${\mathcal{A}}_{CP-}$ have similar magnitudes and opposite signs; their difference corresponds to 3.5~standard deviations. From these values we calculate 68.3\% confidence intervals of ($8.5^{\circ }<\ddot{I}{•}_3<16.5^{\circ }$) or ($84.5^{\circ }<\ddot{I}{•}_3<95.5^{\circ }$) or ($163.3^{\circ }<\ddot{I}{•}_3<171.5^{\circ }$) and $0.321<r_B<0.465$.