Measurement of theB¯0→D*+ℓ−ν¯ℓdecay rate and|Vcb|

We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ based on a sample of about 53 700 ${\overline{B}}^0\to D^{*+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays observed by the BABAR detector. We obtain the branching fraction averaged over $\ell =e,\mu$, $\mathcal{B}({\overline{B}}^0\to D^{*+}{\ell }^{-}{\overline{\nu }}_{\ell })=\mathbf{(}4.90\pm 0.07{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}.)}_{-0.35}^{+0.36}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}.)\mathbf{)}\%$. We measure the differential decay rate as a function of $w$, the relativistic boost $\gamma$ of the $D^{*+}$ in the ${\overline{B}}^0$ rest frame. By extrapolating $d\Gamma /dw$ to the kinematic limit $w\to 1$, we extract the product of $|V_{cb}|$ and the axial form factor ${\mathcal{A}}_1(w=1)$. We combine this measurement with a lattice QCD calculation of ${\mathcal{A}}_1(w=1)$ to determine $|V_{cb}|=\mathbf{(}38.7\pm 0.3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}.)\pm 1.7{(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}.)}_{-1.3}^{+1.5}(\mathrm{\text{theory}})\mathbf{)}\times {10}^{-3}.$