Extraction of $a_1$ and $a_2$ from $B\to \psi K(K^{\ast }),D(D^{\ast })\pi (\rho )$ Decays

Abstract

Based on the factorization approach, we show that the CLEO data for the ratio $\Gamma (B\to \psi K^{\ast })/\Gamma (B\to \psi K)$ and the CDF measurement of the fraction of longitudinal polarization in $B\to \psi K^{\ast }$ can be accounted for by the heavy-flavor-symmetry approach for heavy-light form factors provided that the form factor $F_0$ behaves as a constant, while the $q^2$ dependence is of the monopole form for $F_1,A_0,A_1$, and of the dipole behavior for $A_2$ and $V$. This $q^2$ extrapolation for form factors is further supported by $B\to K^{\ast }\gamma$ data and by a recent QCD-sum-rule analysis. We then apply this method to $B\to D(D^{\ast })\pi (\rho )$ decays to extract the parameters $a_1$ and $a_2$. It is found that $a_1(B\to D^{(\ast )}\pi (\rho ))=1.01\pm 0.06$ and $a_2(B\to D^{(\ast )}\pi (\rho ))=0.23\pm 0.06$. Our result $a_2/a_1=0.22\pm 0.06$ thus significantly improves the previous analysis that leads to $a_2/a_1=0.23\pm 0.11$. We argue that, contrary to what anticipated from the leading $1/N_c$ expansion, the sign of $a_2(B\to \psi \text{K})$ should be positive and $a_2(B\to \psi \text{K}){}_{\sim }^{>}{a}_2(B\to D^{(\ast )}\pi (\rho ))$.

Comments: 14 pages, revised version