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

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.