Dynamical next-to-next-to-leading order parton distributions and the perturbative stability of F_L(x,Q^2)

TL;DR

This paper demonstrates that the perturbative instability of the longitudinal structure function F_L(x,Q^2) at small x is due to standard gluon distributions, and shows that using dynamically generated distributions stabilizes F_L at NNLO for Q^2 ≥ 2-3 GeV^2.

Contribution

It introduces the use of dynamically generated parton distributions at NLO and NNLO, revealing improved perturbative stability of F_L(x,Q^2).

Findings

F_L(x,Q^2) is perturbatively stable with dynamic distributions at NNLO.

Standard gluon distributions cause artificial instability.

Stability achieved for Q^2 ≥ 2-3 GeV^2.

Abstract

It is shown that the previously noted extreme perturbative instability of the longitudinal structure function F_L(x,Q^2) in the small Bjorken-$x$ region, is a mere artefact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).