Belle has observed surprisingly copious production of ψ(3770) in B meson decay B → ψ(3770)K, of which the rate is comparable to that of B → ψ(3686)K. We study this puzzling process in the QCD factorization approach with the effect of S-D mixing considered. We find that the soft scattering effects in the spectator interactions play an essential role. With a proper parametrization for the higher twist soft endpoint singularities associated with kaon, and with the S-D mixing angle θ = −12 • , the calculated decay rates can be close to the data. Implications of these soft spectator effects to other charmonium production in B exclusive decays are also emphasized.
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...
We apply perturbative QCD to the radiative decays of charmonia J/ψ and χcJ into light mesons. We perform a complete numerical calculation for the quark-gluon loop diagrams involved in these processes. The calculated J/ψ decay branching ratios into P-wave mesons f2(1270) and f1(1285) fit the data well, while that of f0(980) (if treated as an ss meson) is predicted to be 1.6 × 10 −4 , which implies that f0(1710) can not be the ss or (uū + dd)/ √ 2 meson. Decays of P-wave charmonia χcJ → ρ(ω, φ)γ (J=0,1,2) are also studied, and the branching ratio of χc1 → ργ is predicted to be 1.4 × 10 −5 , which may be tested by CLEO-c and BESIII with future experiments.Decays of heavy quarkonium into light hadrons are forbidden processes by the OZI rules. The radiative decays of J/ψ into light hadrons such as J/ψ → γf 2 (1270) are expected to proceed via two virtual gluons that subsequently convert to light mesons, with the photon emitted by the charm quarks (see Fig.1 for the three Feynman diagrams). These processes are interesting since they can provide useful information for understanding the fundamental theory of strong interactions, namely, quantum chromodynamics (QCD).In this letter, we will report calculations for radiative decays of charmonia J/ψ and χ cJ into various light mesons based on nonrelativistic quantum chromodynamics. Hopefully, the J/ψ mass is large enough for using perturbative QCD to calculate these processes.Differing from previous works (see, e.g.,[1, 2]), we will perform a complete numerical calculation for the quark-gluon loop diagrams involved in these processes.Here, it is emphasized that in our approach the description of J/ψ as a nonrelativistic cc bound state is a good approximation; while treating the light mesons such as f 2 (1270) as nonrelativistic qq bound states (q = u, d, s) with constituent quark masses m u = m d ≈ 350 M eV, m s ≈ 500 M eV is only an approximation for describing the nonperturbative dynamics that has been used in the nonrelativistic constituent quark models rather successfully, and was also used in previous studies for these radiative decay processes [1,2]. In fact, if the current quark masses for the light quarks, which will vanish in the chiral limit, were used in the quark-gluon loop diagram, we would encounter difficulties with soft and collinear divergences.In the following, we will first focus on the radiative decays of J/ψ to P-wave light mesons such as f 2 (1270), f 1 (1285), and f 0 (980). We adopt the descriptions of nonrelativistic bound states, i.e., both J/ψ and light mesons are described by the color-singlet non-relativistic wave functions. As widely accepted assignments we assume that f 2 (1270) and f 1 (1285) are mainly composed of (uū + dd)/ √ 2 (neglecting the mixing with ss for simplicity). But for f 0 (980), there are many possible assignments such as the tetraquark state, the KK molecule, and the P-wave ss dominated state (for related discussions on f 0 (980) and other scalar mesons, see, e.g., the topical review-note on scalar mesons in [3] and [4]). Si...
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