Nonfactorizable $B\to {\chi }_{c0}K$ decay and QCD factorization

Abstract

We study the unexpectedly large rate for the factorization-forbidden decay $B\to {\chi }_{c0}K$ within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for $B\to {\chi }_{c0}K$ decay is estimated to be in the range $(2-4)\times 10^{-4}$, which is compatible with the Belle and BaBar data.

Comments: Appendix added; it is emphasized that in the dominant twist-3 spectator corrections the end-point singularity contributions may be estimated by the off-shellness of the charm quark (by the binding energy in charmonium) and the gluon (by the transverse momentum of the light quark in the kaon)