Bottomonium Spectrum with Screened Potential

As a sister work of Ref.[1], we incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of bottomonium. We calculate the masses, electromagnetic decays, and E1 transitions of bottomonium states. We find that the fine splittings between $\chi_{bJ}$ (J=0,1,2) states are in good agreement with experimental data, and the E1 transition rates of $\Upsilon(2S)\to\gamma\chi_{bJ}(1P)$ and $\Upsilon(3S)\to\gamma\chi_{bJ}(2P)$ (J=0,1,2) all agree with data within experimental errors. In particular, the mass of $\Upsilon(6S)$ is lowered down to match that of the $\Upsilon(11020)$, which is smaller than the predictions of the linear potential models by more than 100 MeV. Comparison between charmonium and bottomonium in some related problems is also discussed.Comment: 9 pages, Commun. Theor. Phys. (in press

Spin correlations in polarizations of P-wave charmonia χcJ\chi_{cJ} and impact on J/ψJ/\psi polarization

Based on a general form of the effective vertex functions for the decays of P-wave charmonia \chicj, angular distribution formulas for the subsequent decays \chicj\rightarrow \jpsi \gamma and \jpsi \to \mu^+\mu^- are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of \jpsi and muon in the cascade decay \chicj\to\jpsi\gamma\to\mu^+\mu^-\gamma. The \chicj polarization observables are expressed in terms of rational functions of the spin density matrix elements of \chicj production. Generalized rotation-invariant relations for arbitrary integer-spin particles are also derived and their expressions in terms of observable angular distribution parameters are given in the $\chi_{c1}$ and $\chi_{c2}$. To complement our previous direct-\jpsi polarization result, we also discuss the impact on the observable prompt-\jpsi polarization. As an illustrative application of our angular distribution formulas, we present the angular distributions in terms of the tree-level spin density matrix elements of $\chi_{c1}$ and $\chi_{c2}$ production in several different frames at the Large Hadron Collider. Moreover, a reweighting method is also proposed to determine the entire set of the production spin density matrix elements of the $\chi_{c2}$, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.Comment: Version published in PRD, 23 pages, 18 figure

QCD Radiative Correction to the Hadronic Annihilation Rate of 1+−1^{+-} Heavy Quarkonium

Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $\alpha_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelled, and a finite result for the decay width to order $\alpha_s^3$ is then obtained.Comment: 15 pages latex (6 figures included). In this revised version a update reference and acknowledgement are include

S-D mixing and ψ(3770)\psi(3770) production in e+e−e^+e^- annihilation and B decay and its radiative transitions

The large decay rate observed by Belle for $B^+\to\psi(3770)K^+$, which is comparable to $B^+\to\psi(3686)K^+$, might indicate either an unexpectedly large S-D mixing angle $|\theta|\approx 40^o$ or the leading role of the color-octet mechanism in D-wave charmonium production in B decay. By calculating the production rate of $\psi(3770)$ in the continuum $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV with these two possible approaches (i.e. the large S-D mixing and the color-octet mechanism), we show that the measurement for this process at Belle and BaBar may provide a clear cut clarification for the two approaches. In addition, the radiative E1 transition ratio $\Gamma(\psi(3770)\to \gamma\chi_{c2})/\Gamma(\psi(3770)\to \gamma\chi_{c1})$ may dramatically change from $\sim$ 0.04 (for $\theta\approx 0^o$) to $\sim$ 200 (for $\theta\approx -40^o$) due to the large S-D interference effect, thus the E1 transition measurement of $\psi(3770)$ at BES and CLEO-c will also be very useful in clarifying this issue.Comment: final version to appear in Phys.Rev.D, discussion on uncertainties associated with the color-octet matrix elements is added, 16 pages, 2 figure

Photoproduction of ηc\eta_c in NRQCD

We present a calculation for the photoproduction of $\eta_c$ under the framework of NRQCD factorization formalism. We find a quite unique feature that the color-singlet contribution to this process vanishes at not only the leading order but also the next to leading order perturbative QCD calculations and that the dominant contribution comes from the color-octet ${}^1S_0^{(8)}$ subprocess. The nonperturbative color-octet matrix element of ${}^1S_0^{(8)}$ of $\eta_c$ is related to that of ${}^3S_1^{(8)}$ of $J/\psi$ by the heavy quark spin symmetry, and the latter can be determined from the direct production of $J/\psi$ at large transverse momentum at the Fermilib Tevatron. We then conclude that the measurement of this process may clarify the existing conflict between the color-octet prediction and the experimental result on the $J/\psi$ photoprodution.Comment: 11 pages, revtex, 4 ps figure

Peak shifts due to B(∗)−Bˉ(∗)B^{(*)}-\bar{B}^{(*)} rescattering in Υ(5S)\Upsilon(5S) dipion transitions

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 adde