Measurement of the decay $B\to D\ell \hat{I}{½}_{\ell }$ in fully reconstructed events and determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$

Abstract

We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ using the decay $B\to D\ell \hat{I}{½}_{\ell }$ ($\ell =e,\hat{I}¼$) based on 711 fb${}^{-1}$ of $e^{+}{e}^{-}\to \hat{I}\yen (4S)$ data recorded by the Belle detector and containing $772\times 10^6$ $B\bar{B}$ pairs. One $B$ meson in the event is fully reconstructed in a hadronic decay mode while the other, on the signal side, is partially reconstructed from a charged lepton and either a $D^{+}$ or $D^0$ meson in a total of 23 hadronic decay modes. The isospin-averaged branching fraction of the decay $B\to D\ell \hat{I}{½}_{\ell }$ is found to be $\mathcal{B}(B^0\to D^{-}{\ell }^{+}\hat{I}{½}_{\ell })=(2.31\pm 0.03(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$. Analyzing the differential decay rate as a function of the hadronic recoil with the parameterization of Caprini, Lelouch and Neubert and using the form-factor prediction $\mathcal{G}(1)=1.0541\pm 0.0083$ calculated by FNAL/MILC, we obtain $\hat{I}{\cdot }_{\mathrm{EW}}|V_{cb}|=(40.12\pm 1.34)\times 10^{-3}$, where $\hat{I}{\cdot }_{\mathrm{EW}}$ is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parameterization of Boyd, Grinstein and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find $\hat{I}{\cdot }_{\mathrm{EW}}|V_{cb}|=(41.10\pm 1.14)\times 10^{-3}$.

17 pages, 8 figures and 8 tables, submitted to PRD; changes to previous version: updated affiliations, moved introduction of z, added Vcb result without electroweak correction factor