Estimated of $CP$ violation in $B^0$ meson decays into $D^{\ast +}$ and $D^{-}$ mesons

The decay $B^0\to D^{\ast +}{D}^{-}$ is favorable mode for studying $CP$ violation in the interference between mixing and decay for $B^0$ and ${\bar{B}}^0$ mesons. The latest analysis of the $CP$ parameters has been performed by the LHCb collaboration values of $S_{D^{\ast }D}=-0.861\pm 0.077\pm 0.019$, $C_{D^{\ast }D}=-0.059\pm 0.092\pm 0.020$, $\mathrm{△}{S}_{D^{\ast }D}=0.019\pm 0.075\pm 0.012$, $\mathrm{△}{C}_{D^{\ast }D}=-0.031\pm 0.092\pm 0.016$, and ${\mathcal{A}}_{D^{\ast }D}^{CP}=0.008\pm 0.014\pm 0.006\pm 0.003$. We have been estimated the parameters $S_{D^{\ast }D}$ and $C_{D^{\ast }D}$ of the $B^0\to D^{\ast +}{D}^{-}$ decay as $-0.709\pm 0.024$ and $-0.051\pm 0.004$. In the following, we have obtained the values of $\mathrm{△}{S}_{D^{\ast }D}=0.054\pm 0.003$ and $\mathrm{△}{C}_{D^{\ast }D}=0.020\pm 0.001$ and direct $CP$ violation of $0.008\pm 0.001$. Also, we have calculated the branching ratio of $B^0\to D^{\ast +}{D}^{-}$ decay. The values obtained in this work are comparable with the corresponding experimental values.