Determination of the modulus of $\mid V_{cb} \mid$ from the semileptonic decay B$^{0} \rightarrow$ D$*^{-}$l$^{+}\nu$

Semileptonic decays B \rightarrow D^{*-} \ell^+ \nu X were selected from a sample of 3.1 million hadronic Z decays collected by the DELPHI detector at LEP. A topological search for semileptonic B decays to resonant %(D^{**}) and non-resonant D^{*-} \pi^{+} states was performed and the ratio of the branching fractions: \frac {Br ({\mathrm{B} \rightarrow {\mathrm D}^{*-}} \ell^+ \nu X)} {Br({\mathrm{B} \rightarrow {\mathrm D}^{*-}} \ell^+ \nu X) + Br( {\mathrm{B}^0 \rightarrow \mathrm{D}^{*-}} \ell^+ \nu)} = 0.19 \pm 0.10({\mathrm{stat}}) \pm 0.06({\mathrm{syst}}) was determined. Taking into account this contribution, %DB the differential production fraction of the decay the differential decay width of {\mathrm{B}^{0} \rightarrow \mathrm{D}^{*-}} \ell^+ \nu was measured as a function of the momentum transfer from the B to the D^{*-} in two separate analyses, using exclusive and inclusive methods of D^{*-} reconstruction. The distributions were fitted %DB with a linear function over the full momentum transfer range to extract the product of \mathrm{|V_{cb}|} times the normalization of the decay form factor F(q^2_{max}): F(q^2_{max})\mathrm{|V_{cb}|} = (35.0 \pm 1.9({\mathrm{stat}}) \pm 2.3({\mathrm{syst}}) )~\cdot~10^{-3}. The value of \mathrm|V_{cb}| was computed using theoretical calculations of F(q^2_{max}), giving: {\mathrm{|V_{cb}|}} = (38.5 \pm 2.1({\mathrm{stat}}) \pm 2.5({\mathrm{syst}}) \pm 1.7({\mathrm{theory}}))~\cdot~10^{-3}. The total branching fraction Br(\mathrm{B}^{0} \rightarrow D^{*-} \ell^+ \nu) was determined to be: Br ({\mathrm{B}^0 \rightarrow \mathrm{D}^{*-}} \ell^+ \nu) = (5.47 \pm 0.16({\mathrm{stat}}) \pm 0.67({\mathrm{syst}})) \%