Measurement of Differential Distributions of $B\to D^{\ast }\ell \bar{\hat{I}}{½}_{\ell }$ and Implications on $|V_{cb}|$

Abstract

We present a measurement of the differential shapes of exclusive $B\to D^{\ast }\ell \bar{\hat{I}}{½}_{\ell }$ ($B=B^{-},{\bar{B}}^0$ and $\ell =e,\hat{I}¼$) decays with hadronic tag-side reconstruction for the full Belle data set of $711{\mathrm{fb}}^{-1}$ integrated luminosity. We extract the Caprini-Lellouch-Neubert (CLN) and Boyd-Grinstein-Lebed (BGL) form factor parameters and use an external input for the absolute branching fractions to determine the Cabibbo-Kobayashi-Maskawa matrix element and find $|V_{cb}{|}_{\mathrm{CLN}}=(40.1\pm 0.9)\times 10^{-3}$ and $|V_{cb}{|}_{\mathrm{BGL}}=(40.6\pm 0.9)\times 10^{-3}$ with the zero-recoil lattice QCD point $\mathcal{F}(1)=0.906\pm 0.013$. We also perform a study of the impact of preliminary beyond zero-recoil lattice QCD calculations on the $|V_{cb}|$ determinations. Additionally, we present the lepton flavor universality ratio $R_{e\hat{I}¼}=\mathcal{B}(B\to D^{\ast }e\bar{\hat{I}}{½}_e)/\mathcal{B}(B\to D^{\ast }\hat{I}¼\bar{\hat{I}}{½}_{\hat{I}}¼)=0.990\pm 0.021\pm 0.023$, the electron and muon forward-backward asymmetry and their difference $\hat{I}”A_{FB}=0.022\pm 0.026\pm 0.007$, and the electron and muon $D^{\ast }$ longitudinal polarization fraction and their difference $\hat{I}”F_L^{D^{\ast }}=0.034\pm 0.024\pm 0.007$. The uncertainties quoted correspond to the statistical and systematic uncertainties, respectively.