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.