Semileptonic decays $B\to D^{(\ast )}l\nu$ in the perturbative QCD factorization approach

In this paper, we study the $B\to D^{(\ast )}{l}^{-}{\bar{\nu }}_{\mathrm{l}}$ semileptonic decays and calculate the branching ratios ${\cal B}(B \to D^{()} l^- \bar{\nu}_{\rm l})$andtheratios$R(D^{()})$and$R_{\rm D}^{\rm l,\tau}$ by employing the perturbative QCD (pQCD) factorization approach. We find that (a) for $R(D)$ and $R(D^{\ast })$ ratios, the pQCD predictions are $R(D)=0.430_{-0.026}^{+0.021}$, $R(D^{\ast })=0.301\pm 0.013$ and agree well with BaBar’s measurements of $R(D^{(\ast )})$; (b) for the newly defined $R_{\rm D}^{\rm l}$and$R_{\rm D}^{\rm \tau}$ratios,thepQCDpredictionsare$R_{\rm D}^{\rm l} = 0.450^{+0.064}{-0.051}$and$R{\rm D}^{\rm \tau} =0.642^{+0.081}_{-0.070}$, which may be more sensitive to the QCD dynamics of the considered semileptonic decays than $R(D^{(\ast )})$ and should be tested by experimental measurements.