Quasi-PDFs, momentum distributions and pseudo-PDFs

Abstract

We show that 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 $p_3\sim 3$ GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use 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.

Comments: 6 pages, 3 figures, changes in text and references