Transverse Momentum Dependent Distributions from Lattice QCD

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QCD describes the quantum mechanical quark-gluon structure of hadrons like the proton. Knowledge of this structure is important as background information if one wants to interpret, e.g., proton-proton collisions at LHC (CERN), but also because QCD allows to study the full breadth of complex properties of non-Abelean local gauge theories. In the beginning, research focused on collinear physics and simple probability distributions. Meanwhile, research focuses on functions which are sensitive to phase correlations. Among these Transverse Momentum Dependent parton distribution functions (TMDPDFs or simply TMDs) are especially interesting. The projected new electron-ion collider (EIC) in the US will allow to study these in unprecedented detail. However, the experimentally accessable information will be insufficient to pin all TMDs down. (A nucleon has eight different TMDs for each quark flavor and each is a function of Bjorken x and transverse momentum, and in addition there are gluon TMDs.) Therefore, the experimental information must be supplemented by Lattice QCD information. This we want continue to do. A few years ago we were the first to formulate the needed techniques and perform numerical studies and today we collaborate with the leading groups in this field. In addition we plan to calculate the flavour separated quark orbital angular momentum and its scale dependence.