Analysis of deep inelastic scattering with $z$-dependent scale

TL;DR

This paper investigates the impact of using a $z$-dependent scale for the running coupling in deep inelastic scattering evolution, revealing changes in the gluon distribution at low $x$ and $Q^2$, but no improvement in data description.

Contribution

It introduces and explores a $z$-dependent scale for the coupling in NLO DIS evolution, providing new insights into gluon behavior at low $x$ and $Q^2$.

Findings

No improvement in DIS data fit with the new scale.

The gluon distribution at low $x$, low $Q^2$ differs, avoiding the need for a valence-like gluon.

The $z$-dependent scale affects the interpretation of gluon dynamics.

Abstract

Evolution of the parton densities at NLO in $\alpha_S$ using $\tilde W^2 = Q^2 (1-z)/z$ instead of the usual $Q^2$ for the scale of the running coupling $\alpha_S$ is investigated. While this renormalisation scale change was originally proposed as the relevant one for $x \to 1$, we explore the consequences for all $x$ with this choice. While it leads to no improvement to the description of DIS data, the nature of the gluon at low $x$, low $Q^2$ is different, avoiding the need for a `valence-like' gluon.