Cut moments and a generalization of DGLAP equations

TL;DR

This paper introduces a cut Mellin moments approach to analyze deep inelastic scattering, extending the DGLAP equations to new classes of moments that better fit experimental kinematic constraints.

Contribution

It develops a generalized cut Mellin moments framework that satisfies DGLAP equations and can be applied to structure functions within experimental ranges.

Findings

Generalized CMM satisfy DGLAP equations with transformed kernels

Multiple integrations and differentiations of parton distributions are compatible with DGLAP

Suggested classes of CMM are suitable for current experimental kinematic ranges

Abstract

We elaborate a cut (truncated) Mellin moments (CMM) approach that is constructed to study deep inelastic scattering in lepton-hadron collisions at the natural kinematic constraints. We show that generalized CMM obtained by multiple integrations of the original parton distribution $f(x,\mu^2)$ as well as ones obtained by multiple differentiations of this $f(x,\mu^2)$ also satisfy the DGLAP equations with the correspondingly transformed evolution kernel $P(z)$. Appropriate classes of CMM for the available experimental kinematic range are suggested and analyzed. Similar relations can be obtained for the structure functions $F(x)$, being the Mellin convolution $F= C \ast f$, where $C$ is the coefficient function of the process.