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

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 $Q^{2}$.