非相对论量子色动力学(NRQCD)是描述重夸克偶素产生和衰变最成功的理论之一，然而在短程系数计算到QCD次领头阶的情况下，其框架下J/ψ产生的长程矩阵元的普适性尚未被观察到。由于NRQCD框架下，J/ψ产生过程的QCD修正通常比较大，因此更高阶的计算对于检验理论也是必要的。碎裂函数的方法可以有效的避开过于复杂的圈图计算，且能保留在大横动量或大能量区域，高阶贡献中最重要的部分。但由于按定义计算碎裂函数非常困难，现只有极少数碎裂函数有QCD NLO的结果。为克服这种困难，本项目将应用抽取的方法得到胶子和c夸克分别到J/ψ等重夸克偶素的碎裂函数的QCD修正，即计算J/ψ的产生截面，再将此截面与由碎裂图象得到的结果对应，然后抽取碎裂函数。本项目另一个研究内容是将这些碎裂函数应用到具体的过程中，如J/ψ强产生，光产生，在正负电子对撞机上的产生和ηc强产生等，并检验长程矩阵元的普适性。

Nonrelativistic QCD (NRQCD) is one of the most successful theories describing quarkonium productions and decays. Despite its successes in many processes, the universality of the long-distance matrix elements for the J/ψ production has not been verified at QCD next-to-leading-order (NLO) level. Under the NRQCD framework, the QCD corrections to the J/ψ production processes are usually very important, therefore, we expect that the phenomenology would change when higher-order contributions are included. Unfortunately, limited by the computation capability, the next-to-next-to-leading-order results are available for only a few simple processes. Thanks to the fragmentation functions, we can reproduce the dominant contributions at high orders in large transverse momentum regions. A big challenge of this approach is that the calculations of such fragmentation functions are usually very difficult. This project develop an alternative way of obtaining the fragmentation functions, i.e. calculating the QCD corrections to some specific processes for the J/ψ production, such as the J/ψ production in electron-positron annihilation, and the J/ψ production in ηb decay, matching the cross sections (decay widths) with the those obtained by using the fragmentation picture, and extracting the QCD NLO fragmentation functions for the J/ψ production. Further, this project will apply the obtained fragmentation functions to the processes of the J/ψ hadroproduction, photoproduction, the J/ψ production in electron-proton annihilations, and the ηc hadroproduction, and observe the universality of the long-distance matrix elements after the leading-power corrections are embedded in the QCD NLO results.