Measurement of the CKM Matrix Element $|V_{cb}|$ from $B^0\to D^{\ast -}{\ell }^{+}{\nu }_{\ell }$ at Belle

Abstract

We present a new measurement of the CKM matrix element $|V_{cb}|$ from $B^0\to D^{\ast -}{\ell }^{+}{\nu }_{\ell }$ decays, reconstructed with the full Belle data set of $711\mathrm{f}{\mathrm{b}}^{-1}$ integrated luminosity. Two form factor parameterizations, originally conceived by the Caprini-Lellouch-Neubert (CLN) and the Boyd, Grinstein and Lebed (BGL) groups, are used to extract the product $\mathcal{F}(1){\eta }_{\mathrm{EW}}|V_{cb}|$ and the decay form factors, where $\mathcal{F}(1)$ is the normalization factor and ${\eta }_{\mathrm{EW}}$ is a small electroweak correction. In the CLN parameterization we find $\mathcal{F}(1){\eta }_{\mathrm{EW}}|V_{cb}|=(35.06\pm 0.15\pm 0.56)\times 10^{-3}$, ${\rho }^2=1.106\pm 0.031\pm 0.007$, $R_1(1)=1.229\pm 0.028\pm 0.009$, $R_2(1)=0.852\pm 0.021\pm 0.006$. For the BGL parameterization we obtain $\mathcal{F}(1){\eta }_{\mathrm{EW}}|V_{cb}|=(34.93\pm 0.23\pm 0.59)\times 10^{-3}$, which is consistent with the World Average when correcting for $\mathcal{F}(1){\eta }_{\mathrm{EW}}$. The branching fraction of $B^0\to D^{\ast -}{\ell }^{+}{\nu }_{\ell }$ is measured to be $\mathcal{B}(B^0\to D^{\ast -}{\ell }^{+}{\nu }_{\ell })=(4.90\pm 0.02\pm 0.16)\%$. We also present a new test of lepton flavor universality violation in semileptonic $B$ decays, $\frac{\mathcal{B}(B^0\to D^{\ast -}{e}^{+}\nu )}{\mathcal{B}(B^0\to D^{\ast -}{\mu }^{+}\nu )}=1.01\pm 0.01\pm 0.03$. The errors correspond to the statistical and systematic uncertainties respectively. This is the most precise measurement of $\mathcal{F}(1){\eta }_{\mathrm{EW}}|V_{cb}|$ and form factors to date and the first experimental study of the BGL form factor parameterization in an experimental measurement.

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