Problems of QCD factorization in exclusive decays of B meson to charmonium

We study the exclusive decays of $B$ meson into P-wave charmonium states $\chi_{cJ}(J=0,1)$ within QCD factorization approach and find that for $B \to \chi_{c1} K$ decay, the factorization breaks down due to logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order, and the decay rate is too small to accommodate the data, and that for $B\to \chi_{c0} K$ decay, there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic divergences due to spectator interactions even at leading-order. Our results, together with the problem in $B \to J/\psi K$ decay, indicate that QCD factorization can not be safely applied to the exclusive decays of $B$ meson to charmonium.