# New parametrization of the form factors in $\bar{B}\to D\ell\bar{\nu}_\ell$ decays

## TL;DR

This paper introduces a new model-independent parametrization for form factors in ar{B}D\u0000lbar{
u}_l decays, enabling precise extraction of CKM matrix elements and revealing potential ar{B}D bound states.

## Contribution

It proposes a novel parametrization based on phase moments, linking scattering information to form factors, and provides new insights into ar{B}D interactions and states.

## Key findings

- Precise determination of |V_{cb}| and ar{D} ratio.
- Hints of bound and virtual ar{B}D states.
- Formalism applicable to other bc semileptonic decays.

## Abstract

A new model-independent parametrization is proposed for the hadronic form factors in the semileptonic $\bar{B}\to D\ell\bar{\nu}_\ell$ decay. By a combined consideration of the recent experimental and lattice QCD data, we determine precisely the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|=41.01(75)\times 10^{-3}$ and the ratio $\mathcal{R}_D=\frac{\mathcal{BR}(\bar{B}\to D \tau \bar{\nu}_\tau)}{\mathcal{BR}(\bar{B}\to D \ell \bar{\nu}_\ell)}=0.301(5)$. The coefficients in this parametrization, related to phase shifts by sumrulelike dispersion relations and hence called phase moments, encode important scattering information of the $\bar{B}\bar{D}$ interactions which are poorly known so far. Thus, we give strong hints about the existence of at least one bound and one virtual $\bar B \bar D$ $S$-wave $0^+$ states, subject to uncertainties produced by potentially sizable inelastic effects. This formalism is also applicable for any other semileptonic processes induced by the weak $b\to c$ transition.