Critical analysis of theoretical estimates forB-to-light-meson form factors andB→ψK(K*) data using factorization

Abstract

We point out that, if we assume the factorization hypothesis, current estimates of form factors fail to explain the nonleptonic decays B→ψK(${\mathit{K}}^{\mathrm{*}}$) and that the combination of data on the semileptonic decays D→K(${\mathit{K}}^{\mathrm{*}}$)lν and on the nonleptonic decays B→ψK(${\mathit{K}}^{\mathrm{*}}$) (in particular, recent polarization data) severely constrain the form (normalization and ${\mathit{q}}^2$ dependence) of the heavy-to-light-meson form factors. From a simultaneous fit to B→${\mathit{K}}^{\left(\mathrm{*}\right)}$ψ and D→${\mathit{K}}^{\left(\mathrm{*}\right)}$lν data we find that strict heavy quark limit scaling laws do not hold when going from D to B and must have large corrections that make softer the dependence on the masses. We find that ${\mathit{A}}_1$(${\mathit{q}}^2$) should increase slower with ${\mathit{q}}^2$ than ${\mathit{A}}_2$,V,${\mathit{f}}_{+}$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the heavy-to-heavy scaling laws to the heavy-to-light case, complemented with an approximately constant ${\mathit{A}}_1$(${\mathit{q}}^2$). We analyze in the light of these data and theoretical input various theoretical approaches (lattice calculations, QCD sum rules, quark models) and point out the origin of the difficulties encountered by most of these schemes. In particular we check the comptability of several quark models with the heavy quark scaling relations.