Nonperturbative evolution of parton quasi-distributions

Using the formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) F (x , k_⊥²) and quasi-distributions (PQDs) Q (y ,p₃) introduced recently by X. Ji for lattice QCD extraction of parton distributions f (x). We build models for PQDs from the VDF-based models for soft TMDs, and analyze the p₃ dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of p₃ reflecting the transverse momentum dependence of TMDs. Thus, the study of PQDs on the lattice in the domain of strong nonperturbative effects opens a new perspective for investigation of the 3-dimensional hadron structure.