Evolution of the Truncated Mellin Moments of the parton distributions in QCD analysis

Abstract

We review evolution equations for the truncated Mellin moments of the parton distributions and some their applications in QCD analysis. The main finding of the presented approach is that the $n$th truncated moment of the parton distribution obeys also the DGLAP equation but with a rescaled splitting function $P'(z)=z^n P(z)$. This allows one to avoid the problem of dealing with the experimentally unexplored Bjorken-$x$ region. The evolution equations for truncated moments are universal - they are valid in each order of perturbation expansion and can be useful additional tool in analysis of unpolarized as well as polarized nucleon structure functions.