Progress towards a precise ab initio determination of parton structure of hadrons

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This proposal is part of a long term effort of our collaboration to substantially improved the usefulness of Lattice QCD for hadron structure physics. Lattice QCD requires to analytically continue time to imaginary time. This has the unpleasant consequence that only field correlators which are local in time can be straightforwardly evaluated. These are related by operator product expansion to moments of quark and gluon distribution functions. Unfortunately, in practice only the leading few moments can be determined due to numerical noise and operator mixing, which is insufficient for the needs of high luminsity experiments as performed/planned at LHC (CERN, Switzerland), the EIC at BNL (USA), as well as the CEPC and EicC planned in China. A few years ago several alternative approaches have been suggested, which have the potential to change this situation fundamentally, starting with LaMET suggested by Prof. Ji. Related suggestions were already made in the past but without practical consequences. This has changed now. Within the "Lattice Parton Collaboration" (LPC) we systematically test and improve LaMET and expand its applicability. So far this happened on the German side primarily within SFB/TRR-55 "Hadron Physics from Lattice QCD" which will end June,30 2020. This proposal aims at a careful determination of the systematic uncertainties for twist-2 pdfs of the nucleon and meson DAs using CLS configurations and two-loop matching functions which we plan to derive.