Heavy-heavy form factors and generalized factorization

Abstract

Abstract.

We reanalyze \(B\to D\pi\) and \(B \to K J/\psi\) data to extract a set of parameters which give the relevant hadronic matrix elements in terms of factorized amplitudes. Various sources of theoretical uncertainties are studied, in particular those depending on the model adopted for the form factors. We find that the fit to the \(B\to D\pi\) branching ratios substantially depends on the model describing the Isgur-Wise function and on the value of its slope. This dependence can be reduced by substituting the \(BR(B\to D\pi)\) with suitable ratios of non-leptonic to differential semileptonic BRs. In this way, we obtain a model-independent determination of these parameters. Using these results, the \(B\to D\) form factors at \(q^2=M_\pi^2\) can be extracted from a fit of the \(BR(B\to D\pi)\). The comparison between the form factors obtained in this way and the corresponding measurements in semileptonic decays can be used as a test of (generalized) factorization free from the uncertainties due to heavy-heavy form factor modeling. Finally, we present predictions for as-yet-unmeasured \(D\pi\) and \(DK\) branching ratios and extract \(f_{D_s}\) and \(f_{D_s^*}\) from \(B\to DD_s\) decays. We find \(f_{D_s}=270\pm 45\) MeV and \(f_{D_s^*}=260\pm 40\) MeV, in good agreement with recent measurements and lattice calculations.