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

## TL;DR

This paper performs a detailed four-dimensional angular analysis of the decay rom rom B mesons to extract form factors, compare parameterizations, and update key measurements relevant to the CKM matrix element rom.

## Contribution

It introduces a novel unbinned fit method using the Boyd-Grinstein-Lebed approach for form factor extraction in rom decays, showing deviations from previous models and refining key physical parameters.

## Key findings

- Deviations from previous CLN-based form factor fits.
- Updated prediction for rom ratio rom.
- Determination of rom value consistent with exclusive decay averages.

## Abstract

An angular analysis of the decay ${\overline{B} \rightarrow D^\ast \ell^- \overline{\nu}_\ell}$, $\ell\in\{e,\mu\}$, is reported using the full $e^+e^-$ collision data set collected by the \babar experiment at the $\Upsilon(4S)$ resonance. One $B$ meson from the ${\Upsilon(4S)\to B\overline{B}}$ 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 di-lepton 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 $q^2$ parameterization 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 parameterization. The latest form factors also provide an updated prediction for the branching fraction ratio $\mathcal{R}(D^\ast)\equiv \mathcal{B}(\overline{B}\to D^\ast \tau^- \bar{\nu}_\tau)/\mathcal{B}({\overline{B} \rightarrow D^\ast \ell^- \overline{\nu}_\ell})=0.253 \pm 0.005$. Finally, using the well measured branching fraction for the ${\overline{B} \rightarrow D^\ast \ell^- \overline{\nu}_\ell}$ decay, a value of $|V_{cb}|=(38.36\pm 0.90)\times10^{-3}$ is obtained that is consistent with the current world average for exclusive ${\overline{B}\to D^{(\ast)}\ell^- \overline{\nu}_\ell}$ decays and remains in tension with the determination from inclusive semileptonic $B$ decays to final states with charm.