An evaluation of the proton structure functions F2 and FL at small x

We describe the determination of the DIS structure functions F-2 and F-L by using the singlet DokshitzerGribov-Lipatov-Altarelli-Parisi (DGLAP) and Altarelli-Martinelli equations at small values of x. The determination of the longitudinal structure function is presented as a parameterization of F2(x, Q2) and its derivative. Analytical expressions for sigma r(x, Q2) in terms of the effective parameters of the parameterization of F2(x, Q2) and FL(x, Q2) are presented. This analysis is enriched by including the higher-twist effects in calculation of the reduced cross sections which is important at low -x and low -Q2 regions. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable FL(x, Q2) and sigma r(x, Q2) at low x in a wide range of the low absolute four-momentum transfers squared (1.5 GeV2 < Q2 < 120 GeV2) at moderate and high inelasticity. Expanding the method to low and ultra low values of x can be considered in the process analysis of new colliders. We compare the obtained longitudinal structure function with respect to the LHeC simulated uncertainties (Agostini et al. (2020) [4]) with the results from CT18 (Hou et al. (2021) [54]) parametrization model. (C) 2021 The Author(s). Published by Elsevier B.V.