This article describes a determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from the decay $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ using $711{\mathrm{fb}}^{-1}$ of Belle data collected near the ${\rm Y}(4S)$ resonance. We simultaneously measure the product of the form factor normalization $\mathcal{F}(1)$ and the matrix element $|V_{cb}|$ as well as the three parameters ${\rho }^2$, $R_1(1)$ and $R_2(1)$, which determine the form factors of this decay in the framework of the heavy quark effective theory. The results, based on about 120 000 reconstructed $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ decays, are ${\rho }^2=1.214\pm 0.034\pm 0.009$, $R_1(1)=1.401\pm 0.034\pm 0.018$, $R_2(1)=0.864\pm 0.024\pm 0.008$ and $\mathcal{F}(1)|V_{cb}|=(34.6\pm 0.2\pm 1.0)\times {10}^{-3}$. The branching fraction of $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ is measured at the same time; we obtain a value of $\mathcal{B}(B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell })=(4.58\pm 0.03\pm 0.26)\%$. The errors correspond to the statistical and systematic uncertainties. These results give the most precise determination of the form factor parameters and $\mathcal{F}(1)|V_{cb}|$ to date. In addition, a direct, model-independent determination of the form factor shapes has been carried out.

• Received 27 October 2010

DOI:https://doi.org/10.1103/PhysRevD.82.112007