Abstract
In this paper, we have investigated the two body decay of \(B_{s}^{0}\) meson into \(\bar{D}^{*0}\) and \(\phi\) vector mesons which were collected with the LHCb detector for the first time, the branching fraction was measured to be \(\mathcal{B}\left(B_{s}^{0}\to\bar{D}^{*0}\phi\right)=\left(3.7\pm 0.5\pm 0.3\pm 0.2\right)\times 10^{-5}\) . The fraction of longitudinal polarization in this decay was also measured to be \(f_{L}=(73\pm 15\pm 4)\%\) . We have studied the \(B_{s}^{0}\to\bar{D}^{*0}\phi\) decay within the framework of the factorization approach by using three different energy scales, the results obtained for branching fraction from helicity amplitude ( \(\mathcal{A}_{0},\mathcal{A}_{+},\mathcal{A}_{-}\) ) and direct calculation (by omitting helicity \(\pm\) ) at \(\mu=m_{b}\) are \(\left(3.06\pm 0.70\right)\times 10^{-5}\) and \(\left(1.98\pm 0.45\right)\times 10^{-5}\) , respectively. By entering the nonfactorizable contributions the results for branching ratio become \(\left(3.68\pm 0.84\right)\times 10^{-5}\) and \(\left(2.34\pm 0.53\right)\times 10^{-5}\) , at the same scale. We have estimated the fraction of longitudinal polarization in \(B_{s}^{0}\to\bar{D}^{*0}\phi\) decay mode, the result is obtained to be \(f_{L}=(72.64\pm 13.07)\%\) . The most precise determination for the branching fraction of \(B_{s}^{0}\to\bar{D}^{0}\phi\) decay has also been reported by the LHCb collaboration with the value of \(\mathcal{B}\left(B_{s}^{0}\to\bar{D}^{0}\phi\right)=\left(3.0\pm 0.3\pm 0.2\pm 0.2\right)\times 10^{-5}\) . Therefore, we have also calculated the branching ratio of this decay mode without and with entering the QCD corrections and obtained the numerical results as \(\mathcal{B}\left(B_{s}^{0}\to\bar{D}^{0}\phi\right)=\left(1.13\pm 0.24\right)\times 10^{-5}\) and \(\left(1.54\pm 0.35\right)\times 10^{-5}\) . All numerical results are consistent with the experimental values.
