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

We present a new measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ decays, reconstructed with the full Belle data set of $711{\mathrm{fb}}^{-1}$ integrated luminosity. Two form factor parametrizations, 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 parametrization 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 parametrization 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 $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$ is measured to be $\mathcal{B}(B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell })=(4.90\pm 0.02\pm 0.16)\%$. We also present a new test of lepton flavor universality violation in semileptonic $B$ decays, $\frac{\mathcal{B}(B^0\to D^{*-}{e}^{+}\nu )}{\mathcal{B}(B^0\to D^{*-}{\mu }^{+}\nu )}=1.01\pm 0.01\pm 0.03$. The errors quoted 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 parametrization in an experimental measurement.

Figure 1

The $D^{*}$ momenta in the CM frame, for on-resonance and scaled off-resonance data. The dotted line shows the cut applied for suppression of continuum.

Figure 2

Tree level Feynman diagram for $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$.

Figure 3

Definition of the angles ${\theta }_{\ell }$, ${\theta }_{\mathrm{v}}$ and $\chi$ for the decay $B^0\to D^{*-}{\ell }^{+}{\nu }_{\ell }$.

Figure 4

Result of the fits to the ($\cos {\theta }_{B,D*\ell }$, $\mathrm{\Delta }M$, $p_{\ell }$) distributions in the $e$ mode (left) and $\mu$ mode (right). The bin boundaries are discussed in the text. The points are on-resonance data, where the uncertainties are smaller than the markers. The color scheme is defined in the figure.

Figure 5

Results of the fit with the CLN form factor parametrization. The results from the SVD1 and SVD2 samples are added together. The electron modes are on the left and muon modes on the right. The points with error bars are the on-resonance data. Where not shown, the uncertainties are smaller than the black markers. The histograms are, from top to bottom, the signal component, $B\to D^{**}$ background, signal correlated background, uncorrelated background, fake $\ell$ component, fake $D^{*}$ component and continuum.

Figure 6

Results of the fit with the BGL form factor parametrization. The results from the SVD1 and SVD2 samples are added together. The electron modes are on the left and muon modes on the right. The points with error bars are the on-resonance data. Where not shown, the uncertainties are smaller than the black markers. The histograms are, top to bottom, the signal component, $B\to D^{**}$ background, signal correlated background, uncorrelated background, fake $\ell$ component, fake $D^{*}$ component and continuum.