Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$

TL;DR

This paper investigates how different parameterizations of distribution functions affect the calculation of the longitudinal structure function at small x, comparing theoretical models with experimental data and highlighting the impact of nonlinear effects on gluon distributions.

Contribution

It introduces a direct method to extract the longitudinal structure function considering charm and bottom quark contributions, and compares various parametrizations with experimental data.

Findings

Nonlinear effects improve the fit to H1 data at low Q^2.

Comparison shows differences between Mellin transform-based and parametrization models.

Gluon distribution behavior is significantly affected by the parameterization choice.

Abstract

I use a direct method to extract the longitudinal structure function in the next-to-leading order approximation with respect to the number of active flavor from the parametrization of parton distributions. The contribution of charm and bottom quarks corresponding to the gluon distributions (i.e., $G_{n_{f}=3}(x,Q^{2})$ and $G_{n_{f}=5}(x,Q^{2})$) is considered. I compare the obtained longitudinal structure function at $n_{f}=4$ with the H1 data [Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and the result L.P.Kaptari et al.[ Phys.Rev.D{\bf 99}, 096019(2019)] which is based on the Mellin transforms. These calculations compared with the results from CT18 [Phys.Rev.D103, 014013(2021)] parametrization model. The nonlinear effects on the gluon distribution improve the behavior of the longitudinal structure function in comparison with the H1 data and CT18 at low values of $Q^{2}$.