Can $B\to J/\psi K(K^*)$ decays be described by factorization ?

The new measurements of $B\to J/\psi K(K^*)$ decays by CDF and CLEO indicate that the production ratio $R$ and the fraction of longitudinal polarization $\Gamma_L/\Gamma$ are smaller than the previous results. In conjunction with the new result of parity-odd transverse polarization in $B\to J/\psi K^*$, we found a minimal modification to the factorization hypothesis: While the data of $B\to J/\psi K^*$ can be accommodated in the factorization approach with nonfactorizable terms $\chi_{A_1} = \chi_{A_2} = \chi_{V} \equiv \chi$ of order 15%, the result of $R$ measurement requires that the nonfactorizable effect $\chi_{F_1}$ on $B\to J/\psi K$ be slightly larger than $\chi$. Therefore, the effective parameter $a_2^{\rm eff}$ is not universal even for $B\to J/\psi K(K^*)$ decays. We have generalized the considerations to $B\to \psi(2S)K(K^*)$ and $B_s\to J/\psi\phi$ and found that the predictions are in agreement with currently available data.