Determination of the form factors for the decay $B^0\to D^{*-}{l}^{+}{\nu }_l$ and of the CKM matrix element $|V_{cb}|$

We present a combined measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ and of the parameters ${\rho }^2$, $R_1(1)$, and $R_2(1)$, which fully characterize the form factors for the $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ decay in the framework of heavy-quark effective field theory. The results, based on a selected sample of about 52 800 $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ decays, recorded by the BABAR detector, are ${\rho }^2=1.157\pm 0.094\pm 0.027$, $R_1(1)=1.327\pm 0.131\pm 0.043$, $R_2(1)=0.859\pm 0.077\pm 0.021$, and $\mathcal{F}(1)|V_{cb}|=(34.7\pm 0.4\pm 1.0)\times {10}^{-3}$. The first error is the statistical and the second is the systematic uncertainty. Combining these measurements with the previous BABAR measurement of the form factors, which employs a different fit technique on a partial sample of the data, we improve the statistical precision of the result, ${\rho }^2=1.191\pm 0.048\pm 0.028$, $R_1(1)=1.429\pm 0.061\pm 0.044$, $R_2(1)=0.827\pm 0.038\pm 0.022$, and $\mathcal{F}(1)|V_{cb}|=(34.4\pm 0.3\pm 1.1)\times {10}^{-3}$. Using lattice calculations for the axial form factor $\mathcal{F}(1)$, we extract $|V_{cb}|=(37.4\pm 0.3\pm 1.2{\pm }_{1.4}^{1.2})\times {10}^{-3}$, where the third error is due to the uncertainty in $\mathcal{F}(1)$. We also present a measurement of the exclusive branching fraction, $\mathcal{B}=(4.69\pm 0.04\pm 0.34)\%$.