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

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