Pion Electromagnetic Form Factor in the KTK_T Factorization Formulae

Based on the light-cone (LC) framework and the $k_T$ factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In particular, the contribution to the pion form factor from the higher helicity components ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the $k_T$ dependence in the hard amplitude, and that the $k_T$ dependence in LC wavefunction affects the hard and soft contributions substantially. A model for the twist-3 wavefunction $\psi_p(x,\mathbf{k_\perp})$ of the pion has been constructed based on the moment calculation by applying the QCD sum rules, whose distribution amplitude has a better end-point behavior than that of the asymptotic one. With this model wavefunction, the twist-3 contributions including both the usual helicity components ($\lambda_1+\lambda_2=0$) and the higher helicity components ($\lambda_1+\lambda_2=\pm 1$) to the pion form factor have been studied within the modified pQCD approach. Our results show that the twist-3 contribution drops fast and it becomes less than the twist-2 contribution at $Q^2\sim 10GeV^2$. The higher helicity components in the twist-3 wavefunction will give an extra suppression to the pion form factor. When all the power contributions, which include higher order in $\alpha_s$, higher helicities, higher twists in DA and etc., have been taken into account, it is expected that the hard contributions will fit the present experimental data well at the energy region where pQCD is applicable.Comment: 4 pages, 2 figures, Prepared for International Conference on QCD and Hadronic Physics, Beijing, China, 16-20 June 200

Constraints on the Light Pseudoscalar Meson Distribution Amplitudes from Their Meson-Photon Transition Form Factors

The meson-photon transition form factors $\gamma\gamma^*\to P$ ($P$ stands for $\pi$, $\eta$ and $\eta'$) provide strong constraints on the distribution amplitudes of the pseudoscalar mesons. In this paper, these transition form factors are calculated under the light-cone perturbative QCD approach, in which both the valence and non-valence quarks' contributions have been taken into consideration. To be consistent, an unified wavefunction model is adopted to analyze these form factors. It is shown that with proper charm component $f^{c}_{\eta'}\sim -30$ MeV and a moderate DA with $B\sim 0.30$, the experimental data on $Q^{2}F_{\eta\gamma}(Q^2)$ and $Q^{2}F_{\eta'\gamma}(Q^2)$ in whole $Q^2$ region can be explained simultaneously. Further more, a detailed discussion on the form factors' uncertainties caused by the constituent quark masses $m_q$ and $m_s$, the parameter $B$, the mixing angle $\phi$ and $f_{\eta'}^c$ are presented. It is found that by adjusting these parameters within their reasonable regions, one can improve the form factor to a certain degree but can not solve the puzzle for $Q^{2}F_{\pi\gamma}(Q^2)$, especially to explain the behavior of $\pi-\gamma$ form factor within the whole $Q^2$ region consistently. We hope further experimental data on these form factors in the large $Q^2$ region can clarify the present situation.Comment: 18 pages, 8 figures and 1 table. Reference updated. To be published in Phys.Rev.

A Trick to Improve the Efficiency of Generating Unweighted BcB_c Events from BCVEGPY

In the present paper, we provide an addendum to improve the efficiency of generating unweighted events within PYTHIA environment for the generator BCVEGPY2.1 [C.H. Chang, J.X. Wang and X.G. Wu, Comput.Phys.Commun.{\bf 174}, 241(2006)]. This trick is helpful for experimental simulation. Moreover, the BCVEGPY output has also been improved, i.e. one Les Houches Event common block has been added so as to generate a standard Les Houches Event file that contains the information of the generated $B_c$ meson and the accompanying partons, which can be more conveniently used for further simulation.Comment: 4 pages, 2 figures. To be published in Computer Physics Communication

Dominant Spin-Flip Effects for the Hadronic Produced J/ψJ/\psi Polarization at TEVATRON

Dominant spin-flip effects for the direct and prompt $J/\psi$ polarizations at TEVATRON run II with collision energy 1.96 TeV and rapidity cut $|y^{J/\psi}|<0.6$, have been systematically studied, especially, the spin-flip effect for the transition of $(c\bar{c})_8[^3S_1]$ into $J/\psi$ has been carefully discussed. It is found that the spin-flip effect shall always dilute the $J/\psi$ polarization, and with a suitable choice of the parameters $a_{0,1}$ and $c_{0,1,2}$, the $J/\psi$ polarization puzzle can be solved to a certain degree. At large transverse momentum $p_t$, $\alpha$ for the prompt $J/\psi$ is reduced by $\sim50$ for $f_0 = v^2$ and by $\sim80$ for $f_0=1$. We also study the indirect $J/\psi$ polarization from the $b$-decays, which however is slightly affected by the same spin-flip effect and then shall provide a better platform to determine the color-octet matrix elements.Comment: 19 pages, 5 figures. References added. Revised version to be published in Phys.Rev.