An analysis of the longitudinal structure function at next-to-leading order approximation at small-$x$

TL;DR

This paper analyzes the longitudinal structure function at next-to-leading order using an expansion method, showing its dependence on gluon momentum fraction at small x and aligning well with experimental data and modern parametrizations.

Contribution

It applies and extends the expansion method for NLO calculations of the longitudinal structure function across a wide kinematic range, providing insights into gluon dynamics at small x.

Findings

Results agree with H1 experimental data.

Behavior depends on gluon fractional momentum at low x.

Method effectively covers a broad range of x and Q^2.

Abstract

The longitudinal structure function is considered at the next-to-leading order approximation using the expansion method, as defined by M.B.Gay Ducati and P.B.Goncalves [Phys.Lett.B {\bf390}, 401 (1997)] and further developed by Jingxuan Chen et al., [Chin.Phys.C {\bf48}, 063104 (2024)]. This method provides results for a wide range of $x$ and $Q^2$ values. It is observed that the behavior of the longitudinal structure function depends on the fractional momentum carried by gluons at low $x$. The extracted longitudinal structure functions $F_{L}(x,Q^2)$ are in line with data from the H1 Collaboration [V. Andreev et al. (H1 Collaboration), Eur. Phys. J. C 74, 2814 (2014)] and the CT18 parametrization method [T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021)].