Analysis of \(B^0_{(s)}\) Meson Decays Into Two Charm Mesons

In this presentation, we have discussed the two body decays of \(B^0\rightarrow D^{*-}D^{(*)+}_s\) within the quantum chromodynamics (QCD) factorization framework. To calculate the branching fraction of \(B^0\rightarrow D^{*-}D^{*+}_s\) decay we have used helicity amplitudes of \(\mathcal {A}_0,\mathcal {A}_+\) and \(\mathcal {A}_-\). To show the contribution of \(\mathcal {A}_0\), we have calculated the branching ratio using it separately. The results are \(\mathcal {B}(B^0\rightarrow D^{*-}D^{*+}_s)_{\mathcal {A}_0,\mathcal {A}_\pm }={(1.78\pm 0.46)\times 10^{-2}}\) and \(\mathcal {B}(B^0\rightarrow D^{*-}D^{*+}_s)_{\mathcal {A}_0}={(1.05\pm 0.29)\times 10^{-2}}\) and the experimental value is \(\mathcal {B}(B^0\rightarrow D^{*-}D^{*+}_s)=1.77\pm 0.14)\times 10^{-2}\). For the first time, the LHCb collaboration reported the values of all helicity amplitudes and the fraction of longitudinal polarization that is determined to be \(f_L(B^0\rightarrow D^{*-}D^{*+}_s)=0.587\pm 0.010\pm 0.011\), in this paper we have obtained \(\begin{aligned} f_L\end{aligned}\) \(\begin{aligned}(B^0\rightarrow D^{*-}D^{*+}_s)\end{aligned}\) \(\begin{aligned} ={0.599\pm 0.012}\end{aligned}\) . The most precision measurements of the ratio of branching fractions in the \(\begin{aligned} \mathcal {R}_1=\end{aligned}\)\(\begin{aligned}{[\mathcal {B}(B^0\rightarrow D^{*-}D^{*+}_s)}\end{aligned}\)\(\begin{aligned} \times \mathcal {B}(D^{*+}_s\rightarrow D^+_s\gamma )]/\mathcal {B}\end{aligned}\) \(\begin{aligned}(B^0\rightarrow D^{*-} D^+_s)\end{aligned}\) have been reported by LHCb collaboration with the value of \(2.045\pm 0.022\pm 0.071\) and we have achieved \({1.700\pm 0.390}\). In other words, our calculations are in good agreement with the LHCb collaboration reports, and we have also provided the most updated values of these calculations. In the following, we have investigated the two body decay of \(B^0_s\) into \(D^{*-}\) and \(D^+_s\) mesons that its experimental value was reported in 2023 by LHCb group about \((3.90\pm 0.80)\times 10^{-4}\) and we have obtained \((3.96\pm 1.21)\times 10^{-4}\). Also, we have estimated the branching fraction ratio of \(\mathcal {R}_2=\mathcal {B}(B^0_s\rightarrow D^{*-} D^{+}_s)/\mathcal {B}(B^0\rightarrow D^{*-} D^+_s)\) and obtained the numerical result \(0.049\pm 0.015\), while the LHCb collaboration measured to be \(0.049\pm 0.006\pm 0.003\pm 0.002\).