A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation

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.