Philipp Horak ; Christoph Schwanda

19 October 2022

Abstract: We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{cb}$ using the decay $B\to D\ell\nu$ based on $e^+e^-\to\Upsilon(4S)$~data recorded by the Belle II detector and corresponding to \lumi of integrated luminosity. The semileptonic decays \ensuremath{\Bz \to D^{-}(\to K^+ \pi^- \pi^-) \ell^{+} \nu_\ell}\xspace and \ensuremath{\Bp \to \bar D^{0}(\to K^+\pi^-) \ell^{+} \nu_\ell}\xspace are reconstructed, where $\ell$ is either electron or a muon. The second $B$~meson in the $\Upsilon(4S)$~event is not explicitly reconstructed. Using the diamond-frame method, we determine the $B$~meson four-momentum and thus the hadronic recoil. We extract the partial decay rates as functions of $w$ and perform a fit to the decay form-factor and the magnitude of the CKM matrix element $|V_{cb}|$ using the BGL parameterization of the form factor and lattice QCD input from the FNAL/MILC and HPQCD collaborations. We obtain \resVcb, where $\eta_{EW}$ is an electroweak correction, and the error accounts for theoretical and experimental sources of uncertainty.