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

Abstract

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 ${p}_{3}\ensuremath{\gtrsim}3\text{ }\text{ }\mathrm{GeV}$ momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs $\mathcal{P}(x,{z}_{3}^{2})$ that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions $\mathcal{M}(\ensuremath{\nu},{z}_{3}^{2})$, the functions of the Ioffe time $\ensuremath{\nu}={p}_{3}{z}_{3}$ 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 $\ensuremath{\nu}$ dependence remains intact and determines the shape of PDFs.