| Based on the Non-relativistic Quantum Chromodynamics (NRQCD), this thesis carries out the detailed studies on the following several processes related to the heavy quarkonium:1) the inclusive productions of charmonium and bottomonium in the Super-Z factory; 2) the photoproductions of J/ψ in association with a cc pair in the International Linear Collider (ILC); 3) the exclusive productions of bottomonium in association with a photon in the Super-Z factory; 4) the ηc hadroproductions in the Large Hadron Collider (LHC); 5) the hadroproductions and polarizations of J/ψ and ψ in the LHC.The experimental measurements of the J/ψ productions in association with a cc pair in the B factory are not consistent with the NRQCD predictions. Although the next-to-leading order (NLO) QCD corrections almost remedy the gap of the total cross section, the predicted angular distributions are still inconsistent with the data. In addition, recently the LHCb group released the measurements of the J/ψ productions accompanied with a charm hadron which are as well inconsistent with the predictions. In order to test whether the disagreement will appear at other platforms, in this thesis, to begin with, we will carry out the detailed studies on the inclusive productions of J/ψ and other charmonium states in the Super-Z factory, including the total and differential cross sections and the comparisons between the complete calculations and the fragmentation mechanism. It is found that the color octet channels can provide comparable contributions to the color singlet one. In addition, due to the resonance effect of the Z boson, the production rates will be enhanced enormously (when the luminosity is L=1034 cm2s-1, the events/per year is-105). Moreover it is found that the cross section of J/ψ+Xnoncc is much smaller than J/ψ+cc. Besides the studies on J/ψ, the inclusive productions of Y and other bottomonium states are also included and similar phenomenological results are obtained.Then we carry out the complete studies on the prompt J/ψ photoproductions γγâ†'J/ψ+c+c in the ILC which is regarded as the next generation of electron-positron collider, including the total and differential cross sections and the polarization parameter. It is found that the production rates for the photoproduction process are quite sizeable (when L=1034 cm-2s-1, the events/per year is-106). The direct productions are about 78% to the prompt one, ψ feeddown is about 20% and XcJ, feeddown is about 2%. Among the direct productions, the contributions from the color octet channels, especially the 1S08 and 3 PJ8, are at least fifty times bigger than the ones from the color singlet channels. One thing to be mentioned, the predicted distributions of the transverse momentum, rapidity and the polarization parameter from the NRQCD factorization and the color singlet mechanism are far different from each other. Thus the measurements on this concerned processes in ILC, especially on the differential cross sections and the polarization parameter will be very helpful for us to distinguish the color octet from the color singlet and test the color octet mechanism.In addition to the mentioned above problem of the inclusive J/ψ productions, in B factory, the measurements on the exclusive productions of J/ψ are also much bigger than the theoretical predictions. Considering the NLO QCD corrections and the relativistic corrections, the predictions can almost reach the lower limit of the data. Due to the quantum number of the photon is the same with J/ψ, it is interesting to study the channel e+e-â†'ηc(XcJ)+γ.Compared to the charmonium, the bottomonium is more suitable for studying the production mechanism of the heavy quarkonium. It is because that the perturbative calculations for bottomonium is more convergent and the relativistic correction is much smaller than charmonium which can be attributed to that the bottomonium is heavier than the charmonium. However the collision energy of the B factory is too small for bottomonium. Thus in our thesis we carry out the study on the exclusive productions of bottomonium in association with a photon up to NLO accuracy in the Super-Z factory. It is found that the QCD one-loop correction is significant to the leading order (LO) results. i.e. K(Y) â–¡0.72, K(hb) â–¡0.56, K(χb2)â–¡0.48.2014, the LHCb group released the measurements of the ηc hadroproductions. We calculate the corresponding NLO QCD corrections for this process and reproduce the data. Moreover, for the first time, we extract the production ηc color singlet long distance matrix elements (LDMEs) <Oηc(1S10)> by the fit of experiment. Meanwhile we extract the exact range of <Oηc(3S18)>. Then based on the heavy quark spin symmetry (HQSS), we finally obtain <OJ/ψ(3S11)> and the exact range of <OJ/ψ(1S08)> and successfully reproduce the J/ψ polarization data from LHCb.Since the CDF Run I released the measurements on the J/ψ(ψ) polarizations in 2000, the J/ψ and ψ polarization puzzles are considered as one of the most challenging issue to the NRQCD factorization. Thus, with the two recently obtained LDMEs (<OJ/ψ(3S11)> and <OJ/ψ(1S08)>, based on the HQSS and the velocity scaling rules (VSR), adopting the new fitting scheme we calculate the NLO QCD corrections to the hadroproductions of J/ψ,ψ’ and χcJ and finally obtain the rest two color octet LDMEs, namely <OJ/ψ(3S18)> and <OJ/ψ(3PJ8)>. Moreover, we discover the key parameter R which is essential important for the J/ψ(ψ’) polarizations. Eventually, with the new set of LDMEs, we reconcile the chamonium productions and polarizations data in the LHC... |
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