Search

We study the mass spectra of hidden-charm tetraquark systems with quantum numbers $(I^G)J^P=(1^+)1^+$ using QCD sum rules. The analysis incorporates the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the operator product expansions, with particular attention to operator mixing effects due to renormalization group evolution. For the $\bar{d}c\bar{c}u$ system, the masses of two mixed operators, $J_{1,5}^{\text{Mixed}}$ and $J_{2,6}^{\text{Mixed}}$, are determined to be $3.89^{+0.18}_{-0.12}$ GeV and $4.03^{+0.06}_{-0.07}$ GeV, respectively, closely matching those of $Z_c$(3900) and $Z_c(4020)$. Similarly, for the $\bar{s}c\bar{c}u$ states, the masses of $J_{1,5}^{\text{Mixed}}$ and $J_{2,6}^{\text{Mixed}}$ are found to be $4.02^{+0.17}_{-0.09}$ GeV and $4.21^{+0.08}_{-0.07}$ GeV, respectively, in close proximity to $Z_{cs}$(3983)/$Z_{cs}$(4000) and $Z_{cs}$(4220), consistent with the expectation that they are the partners of $Z_c$(3900) and $Z_c$(4020). Our results highlight the crucial role of operator mixing, an inevitable effect in a complete NLO calculation, in achieving a robust phenomenological description for the tetraquark system., Comment: 49 pages, 32 fugures. version accepted for publication in JHEP. arXiv admin note: substantial text overlap with arXiv:2201.11714

Recently LHCb experimental group find an exotic state $T^+_{cc}$ from the process $p\bar{p} \to D^0D^0\pi^+ + X$. A key question is if it is just a molecule or may have confined tetraquark ingredient. To investigate this, different methods are taken, including two channel ($D^{*+}D^0$ and $D^{*0}D^+$) K-matrix unitarization and single channel Flatt\'e-like parametrization method analysed by pole counting rule and spectral density function sum rule. It demonstrates that $T^+_{cc}$ is a molecular state, though the possibility that there may exist elementary ingredient can not be excluded, by rough analysis on its production rate.

It was found that, using nonrelativistic QCD factorization, the predicted $\chi_{cJ}$ hadroproduction cross section at large $p_T$ can be negative. The negative cross sections originate from terms proportional to plus function in ${^{3}\hspace{-0.6mm}P_{J}^{[1]}}$ channels, which are remnants of the infrared subtraction in matching the ${^{3}\hspace{-0.6mm}P_{J}^{[1]}}$ short-distance coefficients. In this article, we find that the above terms can be factorized into the nonperturbative ${^{3}\hspace{-0.6mm}S_{1}^{[8]}}$ soft gluon distribution function in the soft gluon factorization (SGF) framework. Therefore, the problem can be naturally resolved in SGF. With an appropriate choice of nonperturbative parameters, the SGF can indeed give positive predictions for $\chi_{cJ}$ production rates within the whole $p_T$ region. The production of $\psi(2S)$ is also discussed, and there is no negative cross section problem., Comment: 15 pages, 8 figures

A near-threshold enhancement in the $D_s^+ D_s^-$ system, dubbed as $X(3960)$, is observed by the LHCb collaboration recently. A combined analysis on $\chi_{c0}(3930)~(\to D^+ D^-)$, $X(3960)~(\to D_s^+ D_s^-)$, and $X(3915)~(\to J/\psi\omega)$ is performed using both a $K$-matrix approach of $D_{(s)}\bar{D}_{(s)}$ four-point contact interactions and a model of Flatt\'e-like parameterizations. The use of the pole counting rule and spectral density function sum rule indicate, under current statistics, that this $D_s^+ D_s^-$ near-threshold state has probably the mixed nature of a $c\bar{c}$ confining state and $D_s^+ D_s^-$ continuum., Comment: 8 pages, 4 figures, 5 tables

We study the mass spectra of $\bar{Q}Q\bar{Q}Q\ (Q=c,b)$ systems in QCD sum rules with the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Instead of meson-meson or diquark-antidiquark currents, we use diagonalized currents under operator renormalization. We find that differing from conventional mesons $\bar qq$ and baryons $qqq$, a unique feature of the multiquark systems like $\bar{Q}Q\bar{Q}Q$ is the operator mixing or color configuration mixing induced by NLO corrections, which is crucial to understand the color structure of the states. Our numerical results show that the NLO corrections are very important for the $\bar{Q}Q\bar{Q}Q$ system, because they not only give significant contributions but also reduce the scheme and scale dependence and make Borel platform more distinct, especially for the $\bar{b}b\bar{b}b$ in the $\overline{\rm{MS}}$ scheme. We use currents that have good perturbation convergence in our phenomenological analysis. With the $\overline{\rm{MS}}$ scheme, we get three $J^{PC}=0^{++}$ states, with masses $6.35^{+0.20}_{-0.17}$ GeV, $6.56^{+0.18}_{-0.20}$ GeV and $6.95^{+0.21}_{-0.31}$ GeV, respectively. The first two seem to agree with the broad structure around $6.2\sim6.8$ GeV measured by the LHCb collaboration in the $J/\psi J/\psi$ spectrum, and the third seems to agree with the narrow resonance $X(6900)$. For the $2^{++}$ states we find one with mass $7.03^{+0.22}_{-0.26}$ GeV, which is also close to that of $X(6900)$, and another one around $7.25^{+0.21}_{-0.35}$ GeV, which has good scale dependence but slightly large scheme dependence., Comment: 60 pages, 53 figures, nonrelativistic (NR) reductions of some operators are illustrated

We have studied color-octet contributions for $J/\psi$ inclusive production at B factories, i.e., $e^+e^-\to J/\psi(^3P_J^{[8]},^1S_0^{[8]}) + X_{\mathrm{non}-c\bar c}$, using the soft gluon factorization (SGF) approach, in which the $J/\psi$ energy spectrum is expressed in a form of perturbatively calculable short-distance hard parts convoluted with one-dimensional soft gluon distributions (SGDs). The series of velocity corrections originated from kinematic effect can be naturally resummed in this approach. Short-distance hard parts have been calculated analytically to next-to-leading order in $\alpha_s$. Renormalization group equations for SGDs have been derived and solved, which resums Sudakov logarithms originated from soft gluon emissions. Our final result gives a upper bound for color-octet matrix elements consistent with that extracted from hadron colliders. This may relieve the well-known universality problem in the NRQCD factorization. As a comparison, we also analytically calculated short-distance hard parts in the NRQCD factorization, with Sudakov logarithms resummed by using soft collinear effective theory. The comparison shows that velocity corrections from kinematic effect, which have been resummed in SGF, are significant for phenomenological study. Furthermore, it is found that Sudakov logarithms originated from soft gluon emissions are very important, while it is not the case for Sudakov logarithms originated from jet function. Therefore, the partial Sudakov resummation in SGF has already captured the main physics., Comment: 35 pages, 5 figures, published version

We study the triply heavy baryons $\Omega_{QQQ}$ $(Q=c, b)$ in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the $\Omega_{QQQ}$. This is because the NLO not only results in a large correction, but also reduces the parameter dependence, making the Borel platform more distinct, especially for the $\Omega_{bbb}$ in the $\overline{\rm{MS}}$ scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ($\bar {MS}$ and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be $4.53^{+0.26}_{-0.11}$ GeV for $\Omega_{ccc}$ and $14.27^{+0.33}_{-0.32}$ GeV for $\Omega_{bbb}$, where the results are obtained at $\mu=M_B$ with errors including those from the variation of the renormalization scale $\mu$ in the range $(0.8-1.2) M_B$. A careful study of the $\mu$ dependence in a wide range is further performed, which shows that the LO results are very sensitive to the choice of $\mu$ whereas the NLO results are considerably better. In addition to the $\mu=M_B$ result, a more stable value, (4.75-4.80) GeV, for the $\Omega_{ccc}$ mass is found in the range of $\mu=(1.2-2.0) M_B$, which should be viewed as a more relevant prediction in our NLO approach because of $\mu$ dependence., Comment: An auxiliary file added showing calculations of NLO amplitudes; More discussions added on renormalization scale dependence. 12 pages, 6 figures, 5 tables. to be published in Chinese Physics C

We study the fragmentation function of the gluon to color-octet $^3S_1$ heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet $^3S_1$ soft gluon distribution (SGD). The short distance hard part is calculated to next-to-leading order in $\alpha_s$ and a renormalization group equation for the SGD is derived. By solving the renormalization group equation, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study., Comment: 38 pages, 8 figures

The next-to-leading order (NLO) ($\mathcal{O}(\alpha_s^3)$) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ${^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}$ states are calculated within the NRQCD factorization. We use integration-by-parts reduction and differential equations to semi-analytically calculate fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through matching procedure, infrared-safe short distance coefficients and $\mathcal{O}(\alpha_s^2)$ perturbative NRQCD matrix elements $\langle{\mathcal O}^{{^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}}({^{3}\hspace{-0.6mm}S_{1}^{[8]}})\rangle_{\mathrm{NLO}}$ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones., Comment: 19 pages, 6 figures. arXiv admin note: text overlap with arXiv:1810.07656

We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in ${^{1}\hspace{-0.6mm}S_{0}^{[1]}}$ or ${^{1}\hspace{-0.6mm}S_{0}^{[8]}}$ state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of $z$ (light-cone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of $z$, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. $\eta_c$ and $J/\psi$) production at the LHC., Comment: 28 pages, 9 figures

With the QCD sum rules approach, we study the newly discovered doubly heavy baryon $\Xi_{cc}^{++}$. We analytically calculate the next-to-leading order (NLO) contribution to the perturbative part of $J^{P} = \frac{1}{2}^{+}$ baryon current with two identical heavy quarks, and then reanalyze the mass of $\Xi_{cc}^{++}$ at the NLO level. We find that the NLO correction significantly improves both scheme dependence and scale dependence, whereas it is hard to control these theoretical uncertainties at leading order. With the NLO contribution, the baryon mass is estimated to be $m_{\Xi_{cc}^{++}} = 3.66_{-0.10}^{+0.08} \text{~GeV}$, which is consistent with the LHCb measurement., Comment: 13 pages, 6 figures, More detailed calculations are given by adding (1) Appendix A: Analytical Result, (2) Appendix B: Higher Dimensional Operators, (3) An ancillary file for the NLO result with the coefficients related to the master integrals

A comprehensive study on the nature of the $Z_c(3900)$ resonant structure is carried out in this work. By constructing the pertinent effective Lagrangians and considering the important final-state-interaction effects, we first give a unified description to all the relevant experimental data available, including the $J/\psi\pi$ and $\pi\pi$ invariant mass distributions from the $e^+e^-\to J/\psi\pi\pi$ process, the $h_c\pi$ distribution from $e^+e^-\to h_c\pi\pi$ and also the $D\bar D^{*}$ spectrum in the $e^+e^-\to D\bar D^{*}\pi$ process. After fitting the unknown parameters to the previous data, we search the pole in the complex energy plane and find only one pole in the nearby energy region in different Riemann sheets. Therefore we conclude that $Z_c(3900)$ is of $D\bar D^*$ molecular nature, according to the pole counting rule method~[Nucl.~Phys.~A543, 632 (1992); Phys.~Rev.~D 35,~1633 (1987)]. We emphasize that the conclusion based upon the pole counting method is not trivial, since both the $D\bar D^{*}$ contact interactions and the explicit $Z_c$ exchanges are introduced in our analyses and they lead to the same conclusion., Comment: 21 pages, 9 figures. To match the published version in PRD. Additional discussion on the spectral density function is included

We present a complete evaluation for the prompt $\eta_c$ production at the LHC at next-to-leading order in $\alpha_s$ in nonrelativistic QCD. By assuming heavy quark spin symmetry, the recently observed $\eta_c$ production data by LHCb results in a very strong constraint on the upper bound of the color-octet long distance matrix element $1S0$ of $J/\psi$. We find this upper bound is consistent with our previous study of the $J/\psi$ yield and polarization and can give good descriptions for the measurements, but inconsistent with some other theoretical estimates. This may provide important information for understanding the nonrelativistic QCD factorization formulism., Comment: 5 pages, 2 figures, published version in PRL

We study the property of the $X(3872)$ meson by analyzing the $B\to K D\bar D^*$ and $B\to K J/\psi \pi^+\pi^-$ decay processes. The competition between the rescattering mediated through a Breit-Wigner resonance and the rescattering generated from a local $D\bar{D}^* \to D\bar{D}^*$ interaction is carefully studied through an effective lagrangian approach. Three different fits are performed: pure Breit-Wigner case, pure $D\bar{D}^*$ molecule case with only local rescattering vertices (generated by the loop chain), and the mixed case. It is found that data supports the picture where X(3872) is mainly a ($\bar cc$) Breit-Wigner resonance with a small contribution to the self-energy generated by $\bar DD^*$ final state interaction. For our optimal fit, the pole mass and width are found to be: $M_X=3871.2\pm0.7$MeV and $\Gamma_X=6.5\pm1.2$MeV., Comment: 13 pages, 2 figures

We extend our original study in Ref. [1] on the production of $C=+$ charmonium states $X=\eta_c(1S/2S)$ and $\chi_{cJ}(1P/2P)$ in $e^+e^-\to\gamma~+~X$ at B factories to the BEPCII/BESIII energy region with $\sqrt{s}=4.0\mbox{-}5.0$ GeV. In the framework of nonrelativistic QCD factorization, the cross sections are estimated to be as large as $0.1\mbox{-}0.9$ pb. The results could be used to search for the missing $2P$ charmonium states or to estimate the continuum backgrounds in the resonance region., Comment: 10 pages, 2 figures

We evaluate the production cross sections of $X(3872)$ at the LHC and Tevatron at NLO in $\alpha_s$ in NRQCD by assuming that the short-distance production proceeds dominantly through its $\chi_{c1}'$ component in our $\chi_{c1}'\mbox{-}D^0\bar{D}^{*0}$ mixing model for $X(3872)$. The outcomes of the fits to the CMS $p_T$ distribution can well account for the recent ATLAS data in a much larger range of transverse momenta ($10~\mbox{GeV}

We calculate the E1 transition widths of higher vector charmonium states into the spin-triplet 2P states in three typical potential models, and discuss the possibility to detect these 2P states via these E1 transitions. We attempt to clarify the nature of some recently observed X,Y,Z states by comparing them with these 2P charmonium states in these E1 transitions. In particular, the calculated branching ratios of $\psi(4040),\psi(4160)\to \chi^{'}_{c_J}\gamma$ (J=0,1,2) are found to be in the range of $10^{-4}-10^{-3}$, and sensitive to the 3S-2D mixing of $\psi(4040)$ and $\psi(4160)$. The mixing angle may be constrained by measuring $\psi(4040),\psi(4160)\to Z(3930)\gamma$, if Z(3930) is identified with the $\chi^{'}_{c_2}$ state, and then be used in measuring $\chi^{'}_{c_{0,1}}$ states. These processes can be studied experimentally at $e^+e^-$ colliders such as BEPCII/BESIII and CESR/CLEO., Comment: 10 pages, 4 figures

The semi-inclusive B-meson decay into spin-singlet D-wave $2^{-+}$ charmonium, $B\to \eta_{c2}+X$, is studied in nonrelativistic QCD (NRQCD). Both color-singlet and color-octet contributions are calculated at next-to-leading order (NLO) in the strong coupling constant $\alpha_s$. The non-perturbative long-distance matrix elements are evaluated using operator evolution equations. It is found that the color-singlet $^1D_2$ contribution is tiny, while the color-octet channels make dominant contributions. The estimated branching ratio $B(B\to \eta_{c2}+X)$ is about $0.41\,\times10^{-4}$ in the Naive Dimensional Regularization (NDR) scheme and $1.24\,\times10^{-4}$ in the t'Hooft-Veltman (HV) scheme, with renormalization scale $\mu=m_b=4.8$\,GeV. The scheme-sensitivity of these numerical results is due to cancelation between ${}^1S_0^{[8]}$ and ${}^1P_1^{[8]}$ contributions. The $\mu$-dependence curves of NLO branching ratios in both schemes are also shown, with $\mu$ varying from $\frac{m_b}{2}$ to $2m_b$ and the NRQCD factorization or renormalization scale $\mu_{\Lambda}$ taken to be $2m_c$. Comparison of the estimated branching ratio of $B\to \eta_{c2}+X$ with the observed branching ratio of $B \to X(3872)+K$ may lead to the conclusion that X(3872) is unlikely to be the $2^{-+}$ charmonium state $\eta_{c2}$., Comment: Version published in PRD, references added, 26 pages, 9 figures

Using the same quenched limit as input, we compare the charmonium spectra predicted by the coupled-channel model and the screened potential model in the mass region below 4 GeV, in which the contributions from decay channels involving P-wave (as well as even higher excited) D mesons can be neglected. We find that the two models have similar global features in describing charmonium spectrum since they embody the same effect of the vacuum polarization of dynamical light quark pairs. This agreement is encouraging for using the screened potential to further describe the mass spectrum of higher charmonium in the region above 4 GeV. Applying both models will be helpful to clarify the nature of the newly discovered "X,Y,Z" mesons in B-factories and other experiments. In particular, we show the S-wave decay coupling effect on lowering the $\chi_{c1}(2P)$ mass towards the $D\bar {D^*}$ threshold, in support of the assignment of the X(3872) as a $\chi_{c1}(2P)$-dominated charmonium state., Comment: 6 pages, 4 figures

The $\eta$ transitions of $\Upsilon(4S,5S)$ into $\Upsilon(1S,2S)$ are studied in the rescattering model by considering the final state interactions above the $B\bar B$ threshold. The width of the $\eta$ transition of $\Upsilon(4S)$ into $\Upsilon(1S)$ is found to be larger than that of the dipion transition, and the ratio of $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\eta)$ to $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\pi^+\pi^-)$ is predicted to be $R_4=1.8{-}4.5$, which is about two orders of magnitude larger than the expectation of the conventional hadronic transition theory, and is supported by the new BaBar measurement. The widths of the $\eta$ transitions of $\Upsilon(5S)$ are found to be sensitive to the coupling constants $g_{\Upsilon(5S)B^{(*)}B^{(*)}}$ due to a large cancelation between contributions from the $B\bar{B}$, $B^*\bar{B}+c.c.$, and $B^*\bar{B}^*$ channels, and only a rough estimate $\Gamma(\Upsilon(5S)\to\Upsilon(1S,2S)\eta)=10{-}200$ KeV can be given. The widths of the $\eta'$ transitions of $\Upsilon(4S,5S)$ are also discussed, and they could be much smaller than that of the corresponding $\eta$ transitions mainly due to the tiny phase space., Comment: Version published in PRD, 5 pages, 1 figure

We study the energy distributions of dipion transitions $\Upsilon(5S)$ to $\Upsilon(1S,2S,3S)\pi^+\pi^-$ in the final state rescattering model. Since the $\Upsilon(5S)$ is well above the open bottom thresholds, the dipion transitions are expected to mainly proceed through the real processes $\Upsilon(5S)\to B^{(*)}\bar{B}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}\to \Upsilon(1S,2S,3S)\pi^+\pi^-$. We find that the energy distributions of $\Upsilon(1S,2S,3S)\pi^+\pi^-$ markedly differ from that of $\Upsilon(5S)\to B^{(*)}\bar{B}^{(*)}$. In particular, the resonance peak will be pushed up by about 7-20 MeV for these dipion transitions relative to the main hadronic decay modes. These predictions can be used to test the final state rescattering mechanism in hadronic transitions for heavy quarkonia above the open flavor thresholds., Comment: Version published in PRD, energy dependence of the total width in Eq.(12) restored and corresponding figure changed, more discussion and clarification added

In order to explain the observed unusually large dipion transition rates of $\Upsilon(10870)$, the scalar resonance contributions in the re-scattering model to the dipion transitions of $\Upsilon(4S)$ and $\Upsilon(5S)$ are studied. Since the imaginary part of the re-scattering amplitude is expected to be dominant, the large ratios of the transition rates of $\Upsilon(10870)$, which is identified with $\Upsilon(5S)$, to that of $\Upsilon(4S)$ can be understood as mainly coming from the difference between the $p$-values in their decays into open bottom channels, and the ratios are estimated numerically to be about 200-600 with reasonable choices of parameters. The absolute and relative rates of $\Upsilon(5S)\to\Upsilon(1S,2S,3S)\pi^+\pi^-$ and $\Upsilon(5S)\to\Upsilon(1S)K^+K^-$ are roughly consistent with data. We emphasize that the dipion transitions observed for some of the newly discovered $Y$ states associated with charmonia may have similar features to the dipion transitions of $\Upsilon(5S)$. Measurements on the dipion transitions of $\Upsilon(6S)$ could provide further test for this mechanism., Comment: version to appear in Phys. Rev. D, discussions and references added

We study the possibility that the $Z^+(4430)$ state observed by Belle is a $D_1D^*$ (or $D_1'D^*$) resonance in S-wave. Focusing on its decays, We find that the open-charm decay into $D^*D^*\pi$ is dominant. Furthermore, we use the re-scattering mechanism to study its hidden-charm decays and find that the re-scattering effects are significant in $D_1D^*$ channel but not in $D_1'D^*$ channel. For the $J^P=1^-$ candidate, with chosen parameters, we can get $\Gamma(Z^+\to\psi'\pi^+)/\Gamma(Z^+\to J/\psi\pi^+)\thickapprox 5.3$, which tends to account for why the $Z^+(4430)$ is difficult to be found in $J/\psi\pi^+$. However, the $0^-$ candidate can not be ruled out by our calculations., Comment: 5 pages, 2 figures

We re-examine the re-scattering mechanism for the X(3872), as a candidate for the 2P charmonium state $\chi_{c1}(2P)$, decaying to $J/\psi\rho(\omega)$ through exchanging $D^{(*)}$ mesons between intermediate states $D(\bar{D})$ and $\bar{D}^*(D^*)$. We evaluate the dispersive part, as well as the absorptive one, of the re-scattering amplitude and find that the contribution from the dispersive part is dominant even when X(3872) lies above the threshold of the neutral channel $th_n=m_{D^0}+m_{D^{*0}}$. We predict $R_{\rho/\omega}\simeq 1$ for the $m_X$ region scanned by experiments. Meanwhile, we also estimate the rate of $X\to D^0\bar{D}^{0}\pi^0$. Our results favor a charmonium interpretation of X(3872) when it lies slightly below the threshold of $D^0\bar{D}^{*0}$. Furthermore, we evaluated the width of $X\to J/\psi\rho$ with the help of a phenomenological effective coupling constant $g_X$, and find the total width of X(3872) to be in the range of 1-2 MeV., Comment: Version submitted and accepted for publication in PRD; more discussions and references added

We study the factorization-forbidden decays $B\to h_c K$ and $B\to\chi_{c2}K$ in the QCD factorization approach. If neglecting the vertex corrections and regularizing the end-point singularities in spectator corrections properly, we get small branching ratios for both the two decay modes, which are roughly consistent with the experimental upper limits. This is in contrast to another factorization-forbidden decay $B\to \chi_{c0}K$, for which a large decay rate is obtained in the same approach., Comment: 5 pages, 1 figure, presentation of the summary is improved

Belle has observed surprisingly copious production of $\psi(3770)$ in $B$ meson decay $B\to \psi(3770)K$, of which the rate is comparable to that of $B\to \psi(3686)K$. 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 end-point singularities associated with kaon, and with the S-D mixing angle $\theta=-12^{\circ}$, 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., Comment: journal version

$B\to\chi_{c1}(1P,2P)K$ decays are studied in QCD factorization by treating charmonia as nonrelativistic bound states. No infrared divergences exist in the vertex corrections, while the logarithmic end-point singularities in the hard spectator corrections can be regularized by a momentum cutoff. With certain uncertainties we find that the $B\to\chi_{c1}(2P)K$ decay rate can be comparable to $B\to\chi_{c1}(1P)K$, and get $Br(B^0 \to \chi_{c1}' K^0) =Br(B^+ \to \chi_{c1}' K^+)\approx 2\times 10^{-4}$. This might imply a possible interpretation for the newly discovered X(3872) that this state has a dominant $J^{PC} = 1^{++}(2P)$ $c\bar c$ component but mixed with a substantial $D^0\bar{D}^{*0}+D^{*0}\bar{D}^0$ continuum component., Comment: 5 pages, one figure, new value of decay constant f_B=216 Mev used; references added

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., Comment: 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)

In the framework of QCD factorization, we study the $B$ meson exclusive decays $B\to \chi_{cJ}K$ where the spin-triplet P-wave charmonium states $\chi_{cJ}(J=0,1,2)$ are described by the color-singlet non-relativistic wave functions. We find that for these decays (except $\chi_{c1}$) there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet model for charmonia. Unlike in the inclusive decays where the higher Fock states with color-octet $c \bar c$ pair and soft gluon can make contributions to remove the infrared divergences, their contributions can not be accommodated in the exclusive two body decays. As a result, the infrared divergences encountered in exclusive processes involving charmonia may raise a new question to the QCD factorization and NRQCD factorization in B exclusive decays., Comment: 4 pages, revtex, 1 figure

We study the exclusive decays of $B$ meson into pseudoscalar charmonium states $\eta_c$ and $\eta_c^\prime$ within the QCD factorization approach and find that the nonfactorizable corrections to naive factorization are infrared safe at leading-twist order. The spectator interactions arising from the kaon twist-3 effects are formally power-suppressed but chirally and logarithmically enhanced. The theoretical decay rates are too small to accommodate the experimental data. On the other hand, we compare the theoretical calculations for $J/\psi, \psi^\prime$, and $\eta_c, \eta_c^\prime$, and find that the predicted relative decay rates of these four states are approximately compatible with experimental data., Comment: 8 pages, LaTex, 1 figure, one footnote and two references added