Measurement of |V _cb | using the semileptonic decay $\overline{\rm {B^{0}_{d}}} \rightarrow {\rm D}^* \ell^- \overline{\nu}_{\ell}$

Abstract.

Data from Z decays in DELPHI have been searched for $\overline{\rm B^0_d}\rightarrow {\rm D}^{* + } \ell^- \overline{\nu}_{\ell}$ with the ${\rm D}^{* + }$ decaying to ${\rm D}^0 \pi^ +$ and ${\rm D}^0 \rightarrow {\rm K}^- \pi^ +$, ${\rm K}^- \pi^ + \pi^ + \pi^-$ or ${\rm K}^- \pi^ + (\pi^0)$. These events are used to measure the CKM matrix element $\left\vert{\rm V}_{cb} \right\vert$ and the form factor slope, $\rho_{A_1}^2$: ${\cal F}_{D^*}(1) \left\vert{\rm V}_{cb} \right\vert = 0.0392 \pm 0.0018 \pm 0.0023; \rho_{A_1}^2 = 1.32 \pm 0.15 \pm 0.33$ corresponding to a branching fraction: ${\rm BR}(\overline{\rm B^0_d}\rightarrow {\rm D}^{* + } \ell^- \overline{\nu}_{\ell}) = (5.90 \pm 0.22 \pm 0.50)\%.$ Combining these and previous DELPHI measurements gives: ${\cal F}_{D^*}(1)\left|{\rm V}_{cb} \right|= 0.0377 \pm 0.0011 \pm 0.0019,\quad \rho_{A_1}^2 = 1.39 \pm 0.10 \pm 0.33$ and ${\rm BR}(\overline{\rm B^0_d}\rightarrow {\rm D}^{* + } \ell^- \overline{\nu}_{\ell}) = (5.39 \pm 0.11 \pm 0.34)\%$ Using ${\cal F}_{D^*}(1) = 0.91 \pm 0.04$, yields: $\left|{\rm V}_{cb} \right|= 0.0414 \pm 0.0012\textrm{(stat.)} \pm 0.0021\textrm{(syst.)} \pm 0.0018\textrm{(theory)}.$ The b-quark semileptonic branching fraction into a ${\rm D}^{* + }$ emitted from higher mass charmed excited states has also been measured to be: ${\rm BR}(b \rightarrow {\rm D}^{* + } {\rm X} \ell^- \overline{\nu}_{\ell}) = (0.67\pm 0.08\pm0.10)\%$