  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.
