# Cut Moments approach in the analysis of DIS data

## TL;DR

This paper reviews the cut Mellin moments approach to analyze deep inelastic scattering data, providing new tools for testing QCD and extracting sum rules from limited experimental data.

## Contribution

It introduces the generalized CMM approach that overcomes kinematic constraints and constructs a new method to determine the Bjorken sum rule from partial data.

## Key findings

- Successfully applied to COMPASS data on g_1.
- Constructed generalized Bjorken sum rule.
- Demonstrated CMM's effectiveness in QCD tests.

## Abstract

We review the main results on the generalization of the DGLAP evolution equations within the cut Mellin moments (CMM) approach, which allows one to overcome the problem of kinematic constraints in Bjorken $x$. CMM obtained by multiple integrations as well as multiple differentiations of the original parton distribution also satisfy the DGLAP equations with the simply transformed evolution kernel. The CMM approach provides novel tools to test QCD; here we present one of them. Using appropriate classes of CMM, we construct the generalized Bjorken sum rule that allows us to determine the Bjorken sum rule value from the experimental data in a restricted kinematic range of $x$. We apply our analysis to COMPASS data on the spin structure function $g_1$.