The nonfactorizable QED correction to the $\overline{B}_{s}$ ${\to}$ $D_{s}^{(\ast)} {\ell} \bar{\nu}_{\ell}$ decays

Considering the nonfactorizable QED corrections, the branching ratios and ratios of branching ratios $R(D_{s}^{({\ast})})$ for the semileptonic $\overline{B}_{s}$ ${\to}$ $D_{s}^{(\ast)} {\ell} \bar{\nu}_{\ell}$ decays are reevaluated. It is found that (a) the QED contributions can enhance the branching ratios and reduce the ratios $R(D_{s}^{({\ast})})$. (b) The $SU(3)$ flavor symmetry holds basically well in the ratios $R(D)$-$R(D^{\ast})$ for the semileptonic charmed $\overline{B}_{u,d,s}$ decays. (c) The current theoretical uncertainties of branching ratios ${\cal B}(\overline{B}_{s} {\to} D_{s}^{\ast} {\ell} \bar{\nu}_{\ell})$ from the form factors are very large.