B→χc0,2K decays: A model estimation

In this Letter, we investigate the vertex corrections and spectator hard scattering contributions to B→χc0,2K decays, which has no leading contribution from naive factorization scheme. A non-zero binding energy b=2mc−M is introduced to regularize the infrared divergence of the vertex part. The spectator diagrams also contain logarithmic and linear infrared divergences, for which we adopt a model dependent parametrization. If we neglect possible strong phases in the hard spectator contributions, we obtain a too small branching ratio for χc0K while too large one for χc2K, as can be seen from the ratio of the branching ratio of B+→χc2K+ to that of B+→χc0K+, which is predicted to be 2.15−0.76+0.63 in our model, while experimentally it should be about 0.1 or even smaller. But a closer examination shows that, assuming large strong phases difference between the twist-2 and twist-3 spectator terms, together with a slightly larger spectator infrared cutoff parameter Λh, it is possible to accommodate the experimental data. This shows that, for B→χc0,2K decays with no factorizable contributions, QCDF seems capable of producing decay rates close to experiments, in contrast to the B→J/ψK decay which is dominated by the factorizable contributions.