The nonfactorizable QED correction to the ${\bar{B}}_s$ $\to$ $D_s^{(\ast )}\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ decays

Considering the nonfactorizable QED corrections, the branching ratios and ratios of branching ratios $R(D_s^{(\ast )})$ for the semileptonic ${\bar{B}}_s$ $\to$ $D_s^{(\ast )}\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ 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 ${\bar{B}}_{u,d,s}$ decays. © The current theoretical uncertainties of branching ratios $\mathcal{B}({\bar{B}}_s\to D_s^{\ast }\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }})$ from the form factors are very large.