New parametrization of the form factors in $bar{B}to Dellbar{ u}_ell$ decays

A new model-independent parametrization is proposed for the hadronic form factors in the semileptonic $bar{B}to Dellbar{ u}_ell$ 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 $mathcal{R}_D=frac{mathcal{BR}(bar{B}to D tau bar{ u}_tau)}{mathcal{BR}(bar{B}to D ell bar{ u}_ell)}=0.301(5)$. 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 $bto c$ transition.