| Heavy quarkoniums and Bc mesons are heavy-flavor mesons composed by two heavy quarks, and the interaction between two heavy quarks is strong interaction which is described by Quantum Chromodynamics (QCD). Due to the fact that the production and decay of heavy-flavor mesons in high-energy collision experiments can offer important information concerning perturbative QCD and non-perturbative QCD, the study of heavy-flavor mesons is interest and significance in particle physics.It is well known that the hadronization happens at the energy scale ofΛQCD, which is the energy scale of non-perturbative QCD. At present, there is no reliable way to evaluate the hadronic matrix elements, but we can extract some of the physical parameters of non-perturbative QCD from fitting data to investigate the theoretical mechanism. Thus, the precise calculation of the perturbative part in production and decay processes of mesons can improve the accuracy of theoretical predication and strengthen our understanding of non-perturbative QCD. In charpter 1, we briefly introduce the standard model (SM) and some theory widly used in non-perturbative calculation. The method to cancel the infrared singularities, coulomb singularities and P-wave singularities are introduced in charpter 2.OZI-forbidden decay processes of heavy -flavor mesons: J/ψ→η'(η,π0)γ,Υ→η'(η,π0)γand Bc-→η'(η,π0)l-(v|-) are important for studying the bound state. Accurate evaluation of these processes can not only deepen our understanding of OZI rule in PQCD, but also help us to understand the non-perturbative problems. In charpter 3, we have tactfully dealt with these processes and employed light-cone wavefunctions to describe the light mesonsη'(η,π0) under the factorization hypothesis. In the calculation process, we do not take the weak-binding approximation or set the light quark mass to be zero and carry out an accurate integrations of the five- and four-point functions. For J/ψ→η'(η,π0)γandΥ→η(π0)γ, within reasonable ranges of the masses of u, d and s-quarks, the three light cone distribution amplitudes can result quantitatively in agreement with experimental data, but there is an anomaly forΥ→ηγif the present measurement is correct. With regard to the semileptonic OZI-forbidden annihilation decays Bc-→η'(η,π0)l-(v|-), our result show that the branch ratio of Bc-→η'(η,π0)l-(v|-) turns out to be of the order 10-7 - 10-4, which is at the reach of future experiments at LHC. Since heavy quarkonium production at hadron colliders involves strongly interacting partons in the initial state, next-to-leading order (NLO) QCD corrections are expected to be important and crucial in order to reduce the uncertainty of per-turpative QCD theory. In charpter 4, we study associated production of heavy quarkonium and guage boson W at hadron colliders, and find that this process has several unique properties for the test of the color-octet production mechanism. The process is purely a color-octet process up to the next to leading order in perturbative QCD and is dominated by the 3S18 channel, which is important for our study of color-octet mechanism.The main innovations in this thesis are list below:In the calculation of OZI-forbidden decay processes, we do not take the weak-binding approximation or set the light quark mass to be zero and carry out an accurate integrations of the five- and four-point functions, we used light-cone wavefunctions to describe the the light mesonsη'(η,π0) under the factorization hypothesis.We present the calculation of the isospin-violating processes J/ψ(Υ)→π0γ,Bc-→π0l-(v|-) and SU(3) violating processes J/ψ(Υ)→γη8,Bc-→η8l-(v|-). Our results are the most accurate predictions for these processes so far, and they are helpful for our understanding of both perturbative and non-perturbative QCD (the ansatz for light-cone wavefunctions of mesons).Different from the traditional method of using small gluon mass to regularize singularities, we use the dimensional regularization scheme to regularize UV divergences, IR singularities and P state singularities when we perform NLO QCD calculations. We can easily check the cancellation of these singularities in the analytic expressions and get finite results.We use the Two Cutoff Phase Space Slicing Method to calculate the real gluon emission corrections. This method is one of the most reliable methods in performing the calculations of the NLO production of Heavy quarkonium.
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