Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

We show that quasi-parton distribution functions (quasi-PDFs) may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p₃3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x,z₃²) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(ν,z₃²), the functions of the Ioffe time ν=p₃z₃ and the distance parameter z₃² with respect to which it displays perturbative evolution for small z₃. In this form, one may divide out the z₃² dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The ν dependence remains intact and determines the shape of PDFs.