New parametrization of the form factors in $\bar{B}\to D\ell {\bar{\nu }}_{\ell }$ 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 ${\mathcal{R}}_D=\frac{\mathcal{B}\mathcal{R}(\bar{B}\to D\tau {\bar{\nu }}_{\tau })}{\mathcal{B}\mathcal{R}(\bar{B}\to D\ell {\bar{\nu }}_{\ell })}=0.301(5)$. 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.

6 pages, 1 figure, 1 table, version accepted for publication