Introduction

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The only known source of both parity and charge conjugation ($CP$) violation in the Standard Model (SM) of particle physics is described by the unitary 3x3 Cabibbo-Kobayashi-Maskawa (CKM) matrix. The study of $CP$ violation is important as it is necessary for the generation of matter-antimatter asymmetry in the early Universe. The weak decays of hadrons are governed by transition amplitudes $A_f$, proportional to elements of the CKM matrix. A different decay rate of a hadron, such as the $B^+$ meson, compared to its antiparticle is possible if there exists interference of at least two quark-level transition processes.

The $CP$ violation phenomenon is well established experimentally, as it was first observed in neutral kaon decays as early as 1964. In $B$ meson systems, $CP$ violation was first observed in the interference between a decay with and without mixing, and directly in $B^0$ decays. Later, it was also observed in the $B^\pm$ meson decays. Assuming that the asymmetries are small and higher order terms corresponding to products of asymmetries can be neglected, the total $CP$ asymmetry is experimentally determined using $\mathcal{A}^\mathrm{CP} \approx A_\mathrm{raw} - A_\mathrm{P} - A_\mathrm{D}$, where $A_\mathrm{raw}$ is the raw asymmetry, $A_\mathrm{P}$ is the production asymmetry, and $A_\mathrm{D}$ is the asymmetry related to the detection efficiencies. In this paper, only the raw asymmetry is determined using

$$A_\mathrm{raw} \equiv \frac{N(B^+\rightarrow D_{(s)}^{(*)+}\bar{D}^0) - N(B^-\rightarrow D_{(s)}^{(*)-}D^0)}{N(B^+\rightarrow D_{(s)}^{(*)+}\bar{D}^0) + N(B^-\rightarrow D_{(s)}^{(*)-}D^0)},$$

where $N$ is the observed yield in the respective decay mode. The other two asymmetries are obtained from literature.