Nonfactorizable B→χc0KB\to\chi_{c0}K decay and QCD factorization

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

Photoproduction of J/ψJ/\psi in association with a ccˉc\bar{c} pair

Based on the color-singlet model, we investigate the photoproduction of $J/\psi$ associated with a $c \bar{c}$ pair with all subprocesses including the direct, single-resolved, and double-resolved channels. The amplitude squared of these subprocesses are obtained analytically. By choosing corresponding parameters, we give theoretical predictions for the $J/\psi$ transverse momentum distributions both at the LEPII and at the future photon colliders for these subprocesses. The numerical results show that at the LEPII these processes can not give enough contributions to account for the experimental data, and it indicates that the color-octet mechanism may still be needed. At the photon collider with the laser back scattering photons, the resolved photon channe will dominate over the direct one in small and moderate $p_t$ regions with large $\sqrt{s}$. By measuring the $J/\psi$ production associated with a $c\bar{c}$ pair, this process can be separated from the inclusive $J/\psi$ production and may provide a new chance to test the color-singlet contributions.Comment: 16 pages, 7 figure

Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections

We estimate the decay rates of $\eta_c\rightarrow 2\gamma$, $\eta_c'\rightarrow 2\gamma$, and $J/\psi\rightarrow e^+ e^-$, $\psi^\prime\rightarrow e^+e^-$, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these $c\bar{c}$ states. We find that the relativistic correction to the ratio $R\equiv \Gamma (\eta_c \rightarrow 2\gamma)/ \Gamma (J/ \psi \rightarrow e^+ e^-)$ is negative and tends to compensate the positive contribution from the QCD radiative correction. Our estimate gives $\Gamma(\eta_c \rightarrow 2\gamma)=(6-7) ~keV$ and $\Gamma(\eta_c^\prime \rightarrow 2\gamma)=2 ~keV$, which are smaller than their nonrelativistic values. The hadronic widths $\Gamma(\eta_c \rightarrow 2g)=(17-23) ~MeV$ and $\Gamma(\eta_c^\prime \rightarrow 2g)=(5-7)~MeV$ are then indicated accordingly to the first order QCD radiative correction, if $\alpha_s(m_c)=0.26-0.29$. The decay widths for $b\bar b$ states are also estimated. We show that when making the assmption that the quarks are on their mass shells our expressions for the decay widths will become identical with that in the NRQCD theory to the next to leading order of $v^2$ and $\alpha_s$.Comment: 14 pages LaTex (2 figures included

Gluon fragmentation to ^3D_J quarkonia

We present a calculation of the leading order QCD fragmentation functions for gluons to split into spin-triplet D-wave quarkonia. We apply them to evaluate the gluon fragmentation contributions to inclusive ^3D_J quarkonium production at large transverse momentum processes like the Tevatron and find that the D-wave quarkonia, especially the charmonium 2^{--} state, could be observed through color-octet mechanism with present luminosity. Since there are distinctively large gaps between the contributions of two different (i.e, color-singlet and color-octet) quarkonium production mechanisms, our results may stand as a unique test to NRQCD color-octet quarkonium production mechanism.Comment: 15 pages in LaTex (2 figures in PS-file

D-wave heavy quarkonium production in fixed target experiments

We calculate the $D$-wave heavy quarkonium production at fixed target experiments under the NRQCD factorization formalism. We find that the color octet contributions are two orders of magnitude larger than color-singlet contributions if color-octet matrix elements are taken according to the NRQCD velocity scaling rules. Within the theoretical uncertainties, the prediction for the production rate of $2^{--}$ $D$-wave charmonium state agrees with the preliminary result of E705 and other experiments. Searching for the $1^{--}$ $D$-wave state $\psi(3770)$ is further suggested.Comment: 13pages, 4 PS figures, final vertion to appear in PR

Gluonic and leptonic decays of heavy quarkonia and the determination of αs(mc)\alpha_s(m_c) and αs(mb)\alpha_s(m_b)

QCD running coupling constant $\alpha_s(m_c)$ and $\alpha_s(m_b)$ are determined from heavy quarkonia $c\overline{c}$ and $b\overline{b}$ decays. The decay rates of $V\rightarrow 3g$ and $V\rightarrow e^+ e^-$ for $V=J/\psi$ and $\Upsilon$ are estimated by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, and the decay rates are estimated by using the meson wavefunctions which are obtained with a QCD-inspired inter-quark potential. For the $V\rightarrow 3g$ decay we find the relativistic correction to be very large and to severely suppress the decay rate. Using the experimental values of ratio R_g\equiv \frac {\Gamma (V\longrightarrow 3g)}% {\Gamma (V\longrightarrow e^{+}e^{-})}\approx 10,~32 for $V=J/\psi, ~\Upsilon$ respectively, and the calculated widths , we find $\alpha_{s}(m_c)=0.29\pm 0.02$ and $\alpha_s(m_b)=0.20\pm 0.02$. These values for the QCD running coupling constant are substantially enhanced, as compared with the ones obtained without relativistic corrections, and are consistent with the QCD scale parameter $\Lambda_{\overline {MS}}^{(4)}$. We also find that these results are mainly due to kinematic corrections and not sensitive to the dynamical models.Comment: 15 pages in Late

Color-Octet Charmonium Production in Top Quark Decays

We calculate the direct production rate of $J/\psi$ in top quark decays. The color-octet $J/\psi$ production via $t\rightarrow W^+ b J/\psi$ is shown to have a large branching ratio of order $1.5\times 10^{-4}$, which is over an order of magnitude higher than that of the color-singlet $J/\psi$ production via $t\rightarrow W^+ b J/\psi~g~g$ or $t\rightarrow W^+ b~\chi_{cJ}~g$ followed by $\chi_{cJ}\rightarrow J/\psi~\gamma$. This result can be used as a powerful tool to test the importance of the color-octet mechanism in heavy quarkonium production.Comment: 10 pages LaTex (2 figures in PS-file

Possible retardation effects of quark confinement on the meson spectrum

The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so called intrinsic flaw of Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. Good fit for the mass spectrum of both heavy and light quarkomium states is then obtained.Comment: 14 pages in LaTex for

QCD predictions for annihilation decays of P-wave quarkonia to next-to-leading order in αs\alpha_s

The decay rates of P-wave heavy quarkonia to light hadrons are presented to leading order in $v^2$ and next-to-leading order in $\alpha_s$. They include contributions from both the color-singlet component and the color-octet component of quarkonia. Applying these results to charmonium and using measured decay rates for the $\chi_{c1}$ and $\chi_{c2}$ by E760, we determine the two nonperturbative decay matrix elements, and then predict the hadronic decay rates of $\chi_{c0}$ and $h_c$, and the electromagnetic decay rates of $\chi_{c0}$ and $\chi_{c2}$. The obtained decay rates of $\chi_{c0}\to LH$ and $\chi_{c0}\to\gamma\gamma$ are in agreement with the Crystal Ball result, and also with the new measurement by BES. However, the results for $\Gamma(\chi_{c0}\to LH)$ are dependent on the choice of renormalization scale.Comment: 10 pages Latex(5 figures included). We have corrected a numerical error in Eq.(5) and Eq.(11