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

摘要

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? 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x, z2/3) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(ν, z2/3), the functions of the Ioffe time ν = p_3z_3 and the distance parameter z2/3 with respect to which it displays perturbative evolution for small z_3. In this form, one may divide out the z2/3 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.