The nonfactorizable QED correction to the ${\overline{B}}_s$ $\to$ $D_s^{(\ast )}\ell \bar{\hat{I}}{½}_{\ell }$ decays

Abstract

Considering the nonfactorizable QED corrections, the branching ratios and ratios of branching ratios $R(D_s^{(\ast )})$ for the semileptonic ${\overline{B}}_s$ $\to$ $D_s^{(\ast )}\ell \bar{\hat{I}}{½}_{\ell }$ 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 $\mathcal{B}({\overline{B}}_s\to D_s^{\ast }\ell \bar{\hat{I}}{½}_{\ell })$ from the form factors are very large.