Dynamical NNLO 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 NNLO is due to standard gluon distributions, and shows stability when using dynamically generated distributions at Q^2 ≥ 2-3 GeV^2.

Contribution

It reveals that the instability of F_L(x,Q^2) is an artifact of standard gluon distributions and shows stability with dynamically generated distributions at low Q^2.

Findings

F_L(x,Q^2) is perturbatively stable for Q^2 ≥ 2-3 GeV^2 with dynamic distributions.

The instability is due to the choice of gluon distributions, not the perturbative calculation.

Using appropriate distributions improves the reliability of F_L(x,Q^2) predictions.

Abstract

It is shown that the previously noted extreme perturbative NNLO/NLO instability of the longitudinal structure function F_L(x,Q^2) 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).