Measurement of the B[over ¯]^{0}→D^{*+}ℓ^{-}ν[over ¯]_{ℓ} decay rate and |V_{cb}|

We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb| based on a sample of about 53 700 B̅ 0→D*+ℓ-ν̅ ℓ decays observed by the BABAR detector. We obtain the branching fraction averaged over ℓ=e,μ, B(B̅ 0→D*+ℓ-ν̅ ℓ)=(4.90±0.07(stat.)-0.35+0.36(syst.))%. We measure the differential decay rate as a function of w, the relativistic boost γ of the D*+ in the B̅ 0 rest frame. By extrapolating dΓ/dw to the kinematic limit w→1, we extract the product of |Vcb| and the axial form factor A1(w=1). We combine this measurement with a lattice QCD calculation of A1(w=1) to determine |Vcb|=(38.7±0.3(stat.)±1.7(syst.)-1.3+1.5(theory))×10-3.