Nonfactorizable B →χ _{c 0} K Decay and QCD Factorization

Abstract

We study the unexpectedly large rate for the factorization-forbidden decay B → χc0K 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 → χc0K decay is estimated to be in the range (2 − 4) × 10 −4 , which is compatible with the Belle and BaBar data. K [5] were studied in the QCD factorization approach [6] in which the nonfactorizable vertex and spectator corrections were also estimated.To further explore the nonfactorizable contributions it is worth studying the factorization-forbidden decays such as B → χ c0 K. Recently, B → χ c0 K decay has been observed by Belle [7,8] and BaBar [9] with surprisingly large branching ratio which is even comparable to that of the factorization-allowed decay B → χ c1 K:To explain the large decay rate of B → χ c0 K, the final state re-scattering mechanism was suggested [10]. On the other hand, with the Light-Cone Sum Rules [11] the nonfactorizable contributions were found to be too small to accommodate the observed B → χ c0 K decay rate. In fact, in Ref. [5,12] within the QCD factorization approach it was found that for the B → χ c0 K decay, there exist both the infrared (IR) divergences in the vertex corrections and the end-point singularities in the leading twist spectator corrections. This implies that large nonfactorizable contributions may come from soft gluon exchanges. As argued in [12], unlike the inclusive B decays to charmonium, where the IR divergences can be factorized into the color-octet matrix elements associated with the higher Fock states of color-octet cc with soft gluons [13] in nonrelativistic QCD (NRQCD) [14], the IR divergences in the exclusive two-body decays are difficult to be factorized.At the qualitative level, the results of Ref.[13] may suggest that some fraction of the large color-octet contribution in the inclusive B decays to charmonium does in fact end up in two-body decay modes. That is, the soft gluon emitted by the color-octet cc pair may be reabsorbed by the quarks in the kaon or B meson, leading to a possible connection between the color-octet contribution and the infrared behavior of vertex and spectator corrections in QCD factorization approach. So qualitative estimates of these soft gluon contributions are important for understanding the large branching ratios of both B → χ c0 K and B → J/ΨK. Furthermore, since the s quark emitted from the weak vertex moves fast in the B meson rest frame, we may expect that the soft gluon exchange is dominated by that between the cc pair and the spectator quark.In order to estimate the soft gluon con...

New exotic charmonium states

“…The necessity of mixing a cc component with the D 0 D * 0 molecule was already pointed out in some works [27][28][29][30]. In particular, in Ref.…”