pQCD matching functions for lattice calculations of hadron structure

本项目的目的是探索和推广季向东教授最近提出的一种新的利用格点QCD计算强子可观量的方法。这个项目是重要的，因为格点QCD给出的信息是补充什么可以从实验中推导出来。特别是对于像广义部分子分布（GPD），分布振幅（DA）和横向动量相关部分子分布（TMD）这样的复杂对象，实验上可获得的信息不足以确定这些函数。因此，获得一个像核子晶格输入那样的强子的全面图像是至关重要的。目前的格点QCD技术只允许计算某些矩，而不是全函数形式。此外，目前格点QCD结果与核子中等矢量夸克分布函数的二阶矩的实验之间的一致性并不好，这提供了最重要的基准测试。Ji的方法将大部分困难的工作转移到微扰QCD（pQCD）上，即确定纯空间双折射子之间的匹配函数（可以在晶格上计算）和光-除了作为一个热门项目外，这项计划中的研究也希望标志着里根斯堡大学和交通大学之间长期合作的开始。上海该项目包括三个子项目，分别是核子中等矢量夸克分布函数的双圈匹配函数（可能还有一些幂次修正）的计算（SP1），π介子分布振幅的单圈（可能是双圈）匹配函数的计算（SP2），以及Sivers TMD的单圈匹配函数的计算（SP3）。

The aim of this project is to explore and extend a novel approach to the calculation of hadronic observables using lattice QCD, recently proposed by Prof. Xiangdong Ji. This project is important because lattice QCD gives information which is complementary to what can be deduced from experiments. Especially for complicated objects like Generalied Parton Distributions (GPDs), Distribution Amplitudes (DAs) and Transverse Momentum Dependent parton distributions (TMDs) the experimentally obtainable information is insufficient to pin these functions down. Thus, to obtain a comprehensive picture of hadrons like the nucleon lattice input is crucial. Present lattice QCD techniques allow only for the calculation of certain moments put not of the full functional form. In addition the present agreement between lattice QCD results and experiment for the second moment of the isovector quark distribution function in the nucleon, which provides the most important benchmark test, is not good. Ji's method shifts much of the hard work to perturbative QCD (pQCD) namely the determination of matching functions between purely spatial correlators (which can be calculated on the lattice) and the light-cone correlators which are relevant phenomenologically.Besides being a project of topical interest the planned research is also hoped to mark the start of a long term collaboration between Regensburg University and the Jiao Tong University in Shanghai. The project contains three subprojects aiming at the calcuation of the two loop matching function (and possibly some power corrections) for the isovector quark distribution function in the nucleon (SP1),the calculation of the one loop (and possibly two loop) matching function for the pion distribution amplitude (SP2), and the one loop matching function for the Sivers TMD (SP3).