We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from the decay $B\to D\ell {\nu }_{\ell }$ using a $365{\mathrm{fb}}^{-1}$ $e^{+}{e}^{-}\to \mathrm{\Upsilon }(4S)\to B\overline{B}$ data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one $B$ meson is reconstructed in the modes $B^0\to D^{-}(\to K^{+}{\pi }^{-}{\pi }^{-}){\ell }^{+}{\nu }_{\ell }$ and $B^{+}\to {\overline{D}}^0(\to K^{+}{\pi }^{-}){\ell }^{+}{\nu }_{\ell }$, where $\ell$ denotes either an electron or a muon. Charge conjugation is implied. The second $B$ meson in the $\mathrm{\Upsilon }(4S)$ event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable $w=v_B·v_D$, where $v_B$ and $v_D$ are the four-velocities of the $B$ and $D$ mesons. We measure the total decay branching fractions to be $\mathcal{B}(B^0\to D^{-}{\ell }^{+}{\nu }_{\ell })=(2.06\pm 0.05(\mathrm{stat})\pm 0.10(\mathrm{sys}))\%$ and $\mathcal{B}(B^{+}\to {\overline{D}}^0{\ell }^{+}{\nu }_{\ell })=(2.31\pm 0.04(\mathrm{stat})\pm 0.09(\mathrm{sys}))\%$. We probe lepton flavor universality by measuring $\mathcal{B}(B\to De{\nu }_e)/\mathcal{B}(B\to D\mu {\nu }_{\mu })=1.020\pm 0.020(\mathrm{stat})\pm 0.022(\mathrm{sys})$. Fitting the partial decay branching fraction as a function of $w$ and using the average of lattice QCD calculations of the $B\to D$ form factor, we obtain $|V_{cb}|=(39.2\pm 0.4(\mathrm{stat})\pm 0.6(\mathrm{sys})\pm 0.5(\mathrm{th}))\times {10}^{-3}$.

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• Cabibbo–Kobayashi–Maskawa matrix