Measurement of the form factors of the decay $\mathrm{B^0 \to D^{*−} \ell^+ \nu_{\ell}}$ and determination of the CKM matrix element $\mathrm{|V_{cb}|}$

This article describes a determination of the Cabibbo-Kobayashi-Maskawa matrix element |V$_{cb}$| from the decay B$^0$→D*−ℓ$^+$ν$_ℓ$ using 711 fb$^{−}$ of Belle data collected near the $\gamma$(4S) resonance. We simultaneously measure the product of the form factor normalization $F$(1) and the matrix element |V$_{cb}$| as well as the three parameters ρ$^2$, 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$^0$→D*−ℓ$^+$ν$_ℓ$ decays, are ρ$^2$=1.214±0.034±0.009, R$_1$(1)=1.401±0.034±0.018, R$_2$(1)=0.864±0.024±0.008 and $F$(1)|V$_{cb}$|=(34.6±0.2±1.0)×10$^{−3}$. The branching fraction of B$^0$→D*−ℓ$^+$ν$_ℓ$ is measured at the same time; we obtain a value of $B$(B$^0$→D*−ℓ$^+$ν$_ℓ$)=(4.58±0.03±0.26)%. The errors correspond to the statistical and systematic uncertainties. These results give the most precise determination of the form factor parameters and F(1)|V$_{cb}$| to date. In addition, a direct, model-independent determination of the form factor shapes has been carried out.