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 (Accardi et al. in Phys Rev D 93:114017, 2016) parametrization model. The obtained results with the Bjorken variable of x are found to be comparable with the results Kaptari et al. (Phys Rev D 99:096019, 2019) which is based on the Mellin transform techniques.