Parton pseudo-distributions and their evolution

  We  study evolution of parton pseudo-distributions using the data of exploratory lattice calculations 
 by Orginos et al.   We extend the analysis beyond the  leading-logarithm analysis by  incorporating recent  calculations of   one-loop corrections  for the reduced  Ioffe-time pseudo-distribution ${\mathfrak M} (\nu,z_3^2)$.   We   observe  that the one-loop   corrections contain a  large term reflecting the fact that effective distances involved in  the  most important diagrams are much smaller than the nominal distance $z_3$.  We find that the    large  correction in this  case may be absorbed into the  evolution term. As a result,   the perturbative expansion used for extraction of
$\overline{\rm MS}$-scheme   parton densities    at the $\mu \approx 2$ GeV scale   is  under control.  The   extracted   parton distribution   is rather close to  global fits  in the $x>0.1$ region,  but deviates from them for  $x<0.1$.