Extraction of ${\mathit{a}}_1$ and ${\mathit{a}}_2$ from B→ψK(${\mathit{K}}^{\mathrm{*}}$), D(${\mathit{D}}^{\mathrm{*}}$)π(ρ) decays

Based on the factorization approach, we show that the CLEO data for the ratio Γ(B→ψ${\mathit{K}}^{\mathrm{*}}$)/Γ(B→ψK) and the CDF measurement of the fraction of longitudinal polarization in B→ψ${\mathit{K}}^{\mathrm{*}}$ can be accounted for by the heavy-flavor-symmetry approach for heavy-light form factors provided that the form factor ${\mathit{F}}_0$ behaves as a constant, while the ${\mathit{q}}^2$ dependence is of the monopole form for ${\mathit{F}}_1$, ${\mathit{A}}_0$, ${\mathit{A}}_1$, and of the dipole behavior for ${\mathit{A}}_2$ and V. This ${\mathit{q}}^2$ extrapolation for form factors is further supported by B→${\mathit{K}}^{\mathrm{*}}$γ data and by a recent QCD sum-rule analysis. We then apply this method to B→D(${\mathit{D}}^{\mathrm{*}}$)π(ρ) decays to extract the parameters ${\mathit{a}}_1$ and ${\mathit{a}}_2$. It is found that ${\mathit{a}}_1$(B→${\mathit{D}}^{\left(\mathrm{*}\right)}$π(ρ))=1.01±0.06 and ${\mathit{a}}_2$(B→${\mathit{D}}^{\left(\mathrm{*}\right)}$π(ρ))=0.23±0.06. Our result ${\mathit{a}}_2$/${\mathit{a}}_1$=0.22±0.06 thus significantly improves the previous analysis that leads to ${\mathit{a}}_2$/${\mathit{a}}_1$=0.23±0.11. We argue that, contrary to what is anticipated from the leading 1/${\mathit{N}}_{\mathit{c}}$ expansioon, the sign of ${\mathit{a}}_2$(B→ψ${\mathit{K}}^{\left(\mathrm{*}\right)}$) should be positive and ${\mathit{a}}_2$(B→ψ${\mathit{K}}^{\left(\mathrm{*}\right)}$)≳${\mathit{a}}_2$(B→