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 p(3) greater than or similar to 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x, z(3)(2)) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(nu, z(3)(2)) the functions of the Ioffe time nu = p(3)z(3) and the distance parameter z(3)(2) with respect to which it displays perturbative evolution for small z(3). In this form, one may divide out the z(3)(2) dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The nu dependence remains intact and determines the shape of PDFs.