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

TL;DR

This paper reviews the evolution equations for truncated Mellin moments of parton distributions in QCD, highlighting a rescaled splitting function that simplifies analysis by avoiding the unmeasured Bjorken-x region.

Contribution

It introduces a universal evolution equation for truncated moments with a rescaled splitting function, applicable across all perturbation orders in QCD analysis.

Findings

Truncated Mellin moments obey DGLAP equations with a rescaled splitting function.

The approach simplifies analysis by excluding unmeasured Bjorken-x regions.

Evolution equations are valid for both polarized and unpolarized structure functions.

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.