Parton distribution functions provide an important insight into the inner structure of hadrons, by giving information on the momentum and spin distribution of partons. Extracting parton distribution functions (PDFs) directly from Lattice QCD has been thought impossible, since they are given in terms of non-local light cone correlations in Minkowski space-time and light-like distances are not accessible on a Euclidean lattice. Recently a new approach was proposed to compute quasi-distributions. It requires the computation of purely spatial correlations, which is completely feasible with lattice methods. We present results for the iso-vector combination for the unpolarized, helicity and transversity quasi-distributions, obtained with $N_f=2$ twisted mass clover-improved fermions at the physical pion mass and discuss their matching to the physical PDFs.

Hadron Structure