pQCD matching functions for lattice calculations of hadron structure

这个项目的目的是探索和扩展一种新的方法来计算强子可观测值使用晶格QCD，最近由吉向东教授提出。这个项目很重要，因为晶格QCD提供的信息是可以从实验中推断出来的补充。特别是对于像广义部子分布（gpd）、分布振幅（DAs）和横向动量相关部子分布（TMDs）这样的复杂对象，实验获得的信息不足以确定这些函数。因此，获得像核子晶格输入这样的强子的全面图像是至关重要的。目前的晶格QCD技术只允许计算某些矩，而不是全函数形式的矩。此外，目前晶格QCD的结果与提供最重要的基准测试的核子中等矢量夸克分布函数的第二矩的实验结果不太吻合。Ji的方法将大部分艰苦的工作转移到微扰QCD （pQCD）上，即确定纯空间相关器（可以在晶格上计算）和光锥相关器（在现象学上相关）之间的匹配函数。除了是一个热门的研究项目外，这个计划中的研究也标志着雷根斯堡大学和上海交通大学之间长期合作的开始。本项目包含三个子项目，分别是计算核子中等矢量夸克分布函数（SP1）的双环匹配函数（可能还有一些功率修正），计算介子分布振幅（SP2）的单环（可能还有双环）匹配函数，以及计算Sivers TMD的单环匹配函数（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).