A determination of the longitudinal structure function $F_{L}$ from the parametrization of $F_{2}$ based on the Laplace transformation

TL;DR

This paper derives the longitudinal structure function $F_{L}$ from the parametrization of $F_{2}$ using Laplace transforms, considering charm quark mass effects, and compares results with experimental data and other models.

Contribution

It introduces a novel Laplace transform method to calculate $F_{L}$ from $F_{2}$ parametrization, including charm mass effects, and validates results against experimental data.

Findings

Results agree with H1 and CJ parametrizations.

Including charm mass affects the $F_{L}$ calculation.

Method is comparable to Mellin transform approaches.

Abstract

I calculate the longitudinal structure function, using Laplace transform techniques, from the parametrization of the structure function $F_{2}(x,Q^{2})$ and its derivative at low values of the Bjorken variable $x$. I consider the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_{f}=4$. The results are compared with the H1 collaboration data and the CTEQ-Jefferson Lab (CJ) collaboration [Phys.Rev.D {\bf93}, 114017 (2016)] parametrization model. The obtained results with the Bjorken variable of $x$ are found to be comparable with the results L.P.Kaptari et al. [Phys.Rev.D {\bf99}, 096019 (2019)] which is based on the Mellin transform techniques.