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The $\bar{B}_s^0 \to D_s^{(*)+} l^- \bar{\nu}_l$ semileptonic decays werecalculated in the framework of the standard model (SM) by employing theperturbative QCD (pQCD) factorization approach. We defined four ratios of thebranching ratios of the considered decays $R(D_s^{(*)})$ and$R_{D_s}^{l,\tau}$. From the numerical results and phenomenological analysis wefound that: (a) The pQCD predictions for the branching ratios $Br(\bar{B}_s^0\to D_s^{(*)+} l^-\bar{\nu}_l)$ generally agree well with the previoustheoretical predictions; (b) For the four ratios, the pQCD predictions are$R(D_s)= 0.392 \pm 0.022$, $R(D_s^{*})= 0.302\pm 0.011$,$R_{D_{s}}^l=0.448^{+0.058}_{-0.041}$ and$R_{D_{s}}^\tau=0.582^{+0.071}_{-0.045}$, which show a very good $SU(3)_F$flavor symmetry with the corresponding ratios for $B\to D^{(*)} l^-\bar{\nu}_l$ decays; and (c) we strongly suggest the measurements of the newratios $R(D_s^{(*)})$ and $R_{D_{s}}^{l,\tau}$ in the forthcoming Super-Bexperiments.

Study of $\bar{B}_s^0 \to (D_s^+,D_s^{*+}) l^-\bar{\nu}_l$ decays in the pQCD factorization approach