Determination of $|V_{cb}|$ from $B\to D\ell \hat{I}½$ decays using 2019-2021 Belle II data

Abstract

We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{cb}$ using $B\to D\ell \hat{I}½$ decays. The result is based on $e^{+}{e}^{-}\to \hat{I}\yen (4S)$ data recorded by the Belle II detector corresponding to 189.2/fb of integrated luminosity. The semileptonic decays $B^0\to D^{-}(\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{-}){\ell }^{+}\hat{I}{½}_{\ell }$ and $B^{+}\to {\bar{D}}^0(\to K^{+}\ddot{I}{€}^{-}){\ell }^{+}\hat{I}{½}_{\ell }$ are reconstructed, where $\ell$ is either electron or a muon. The second $B$ meson in the $\hat{I}\yen (4S)$ 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 CKM parameter $|V_{cb}|$ using the BGL parameterization of the form factor and lattice QCD input from the FNAL/MILC and HPQCD collaborations. We obtain $\hat{I}{\cdot }_{EW}|V_{cb}|=(38.53\pm 1.15)\times 10^{-3}$, where $\hat{I}{\cdot }_{EW}$ is an electroweak correction, and the error accounts for theoretical and experimental sources of uncertainty.

20 pages, 4 figures