Quasi-Parton Distribution Fuctions, 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 p3 ≳ 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x, z²3) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(v, z²3), the functions of the Ioffe time v = p3z3 and the distance parameter z²3 with respect to which it displays perturbative evolution for small z3. In this form, one may divide out the z²3 dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The v dependence remains intact and determines the shape of PDFs