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

Abstract

We study the exclusive decays of $B$ meson into P-wave charmonium states ${\chi }_{cJ}(J=0,1)$ in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For $B\to {\chi }_{c1}K$ decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For $B\to {\chi }_{c0}K$ decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to $B$-meson exclusive decays to charmonium states.

Latex, 7 pages, 1 eps figure, final version to appear in Phys.Lett.B; a few references are added, the expression of chi_c1 decay constant is given

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