Determination of $|V_{cb}|$ using $B\to D\ellν_\ell$ Decays at Belle II

Abstract

We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from the decay $B\to D\ellν_\ell$ using a $365~\mathrm{fb}^{-1}$ $e^+e^-\toΥ(4S)\to B\bar B$ data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one $B$ meson is reconstructed in the modes $B^0\to D^-(\to K^+π^-π^-)\ell^+ν_\ell$ and $B^+\to \bar D^0(\to K^+π^-)\ell^+ν_\ell$, where $\ell$ denotes either an electron or a muon. Charge conjugation is implied. The second $B$ meson in the $Υ(4S)$ event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable $w=v_B\cdot v_D$, where $v_B$ and $v_D$ are the 4-velocities of the $B$ and $D$ mesons. We measure the total decay branching fractions to be $\mathcal{B}(B^0\to D^-\ell^+ν_\ell)=(2.06 \pm 0.05\,(\mathrm{stat.}) \pm 0.10\,(\mathrm{sys.}))\%$ and $\mathcal{B}(B^+\to\bar D^0\ell^+ν_\ell)=(2.31 \pm 0.04\,(\mathrm{stat.}) \pm 0.09\,(\mathrm{sys.}))\%$. We probe lepton flavor universality by measuring $\mathcal{B}(B\to Deν_e)/\mathcal{B}(B\to Dμν_μ)=1.020 \pm 0.020\,(\mathrm{stat.})\pm 0.022\,(\mathrm{sys.})$. 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}$.

Figures (3)

• Figure 1: Distribution of $\cos\theta_{BY}$ after signal selection shown separately for the charged and neutral modes and electron and muon events. The Belle II data are the points with error bars. The stacked histograms show the expected distributions prior to the fit, normalized to the luminosity and after applying the corrections described in Sec. \ref{['sec:corrections']}. Section \ref{['sec:fit']} describes the different components. The hatched area represents the statistical and systematic uncertainties of the simulated samples. The panels at the bottom of each distribution show the difference between data and simulation divided by the combined uncertainty.
• Figure 2: Fitted distributions of $\cos\theta_{BY}$ in bins of $w$ in the $D^0e$, $D^0\mu$, $D^+e$ and $D^+\mu$ samples. The two-dimensional distribution in $(\cos\theta_{BY}, w)$ is "unrolled", such that each group of bins corresponds to $\cos\theta_{BY}$ in a given $w$ interval, with successive groups representing increasing $w$ bins. The Belle II data are the points with error bars. The stacked histograms are simulated events normalized according to the fit result. Sec. \ref{['sec:fit']} describes the different components. The panels at the bottom of each distribution show the difference between data and fit results, divided by the statistical uncertainty.
• Figure 3: Form factor resulting from the fit described in Sec. \ref{['sec:bcl']} compared to the measurement of $\Delta\Gamma_i/\Delta w$ (Table \ref{['tab:dGdw']}). The uncertainty on $\eta_{\rm EW}|V_{cb}|$ shown represents the total uncertainty from statistical, systematic, and theoretical sources, as directly obtained from the fit, prior to decomposition into individual components.