pQCD matching functions for lattice calculations of hadron structure

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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).