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

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