Extraction of form Factors from a Four-Dimensional Angular Analysis of $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$

An angular analysis of the decay $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$, $\ell \in \{e,\mu \}$, is reported using the full $e^{+}{e}^{-}$ collision data set collected by the BABAR experiment at the $\mathrm{\Upsilon }(4S)$ resonance. One $B$ meson from the $\mathrm{\Upsilon }(4S)\to B\overline{B}$ decay is fully reconstructed in a hadronic decay mode, which constrains the kinematics and provides a determination of the neutrino momentum vector. The kinematics of the semileptonic decay is described by the dilepton mass squared, $q^2$, and three angles. The first unbinned fit to the full four-dimensional decay rate in the standard model is performed in the so-called Boyd-Grinstein-Lebed approach, which employs a generic $q^2$ parametrization of the underlying form factors based on crossing symmetry, analyticity, and QCD dispersion relations for the amplitudes. A fit using the more model-dependent Caprini-Lellouch-Neubert (CLN) approach is performed as well. Our form factor shapes show deviations from previous fits based on the CLN parametrization. The latest form factors also provide an updated prediction for the branching fraction ratio $\mathcal{R}(D^{*})\equiv \mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })=0.253\pm 0.005$. Finally, using the well-measured branching fraction for the $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ decay, a value of $|V_{cb}|=(38.36\pm 0.90)\times {10}^{-3}$ is obtained that is consistent with the current world average for exclusive $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays and remains in tension with the determination from inclusive semileptonic $B$ decays to final states with charm.

Figure 1

Comparisons between data and generic $B\overline{B}$ simulation in the discriminating variables (a) $U$ and (b) $E_{\mathrm{extra}}$. For each plot, selections in all other variables have been applied.

Figure 2

Comparison between the BABAR BGL-CLN and CLN WA [19] form factors $\{A_1,A_2,V\}$. Also shown is the LCSR prediction at $q^2=0$ [22]. The error bands are depicted by the dashed curves and include both statistical and systematic uncertainties.

Figure 3

Comparisons as binned scatter plots between the BABAR data (top row) and simulation weighted by the BGL fit result (bottom row) in (a) backward, (b) mid, and (c) forward angles in $\cos {\theta }_{\ell }$. The multidimensional features in the data are well represented by the model. The $z$ axes indicate the number of events in each bin and the simulation is normalized to the number of data events.