Nonfactorizable contributions to $B$ meson decays into charmonia

Abstract

We analyze the $B\to (J/\psi ,{\chi }_{c0},{\chi }_{c1},{\eta }_c)K^{(\ast )}$ decays, which have small or even vanishing branching ratios in naive factorization assumption (FA). We calculate nonfactorizable corrections to FA in the perturbative QCD approach based on $k_T$ factorization theorem. The charmonium distribution amplitudes are inferred from the non-relativistic heavy quarkonium wave functions. It is found that the nonfactorizable contributions enhance the branching ratios and generate the relative phases among helicity amplitudes of the above modes. Most of the observed branching ratios, polarization fractions, and relative phases, except those of $B\to {\eta }_{c}K$, are explained. Our predictions for the $B\to ({\chi }_{c0},{\chi }_{c1},{\eta }_c)K^{\ast }$ decays can be compared with future data.

Comments: 25 pages, 2 figures, Refs added, typos corrected, version to appear in Phys. Rev. D