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 χcJ(J = 0, 1) within QCD factorization approach and find that for B → χc1K 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 → χc0K 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 → J/ψK decay, indicate that QCD factorization can not be safely applied to the exclusive decays of B meson to charmonium. PACS numbers: 13.25.Hw; 14.40.Gx Exclusive nonleptonic B-meson decays provide the opportunity to determine the parameters of the CKM matrix, to explore CP violation and to observe new physics effects. However, quantitative understanding of nonleptonic B-meson decays is difficult due to stronginteraction effects. Beneke et al. have considered two-body nonleptonic B-meson decays extensively including a light-light as well as a heavy-light final states[1, 2, 3]. The general idea is that in the heavy quark limit mb ≫ ΛQCD, the transition matrix elements of operators in the hadronic decay B → M1M2 with M1 being the recoiled meson and M2 being the emitted meson are given by[2] 〈M1M2|Oi|B〉 = 〈M1|j1|B〉〈M2|j2|0〉 [ 1 + ∑ rnα n s +O( ΛQCD mb ) ]