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.