An analysis of the longitudinal structure function at next-to-leading order approximation at small-x*

Abstract The longitudinal structure function is considered as the next-to-leading order approximation using the expansion method, defined by Ducati and Goncalves [Phys. Lett. B 390 , 401 (1997)] and further developed by Chen et al . [Chin. Phys. C 48 , 063104 (2024)]. This method provides results for a wide range of x and values. The longitudinal structure function has been observed to depend on the fractional momentum carried by gluons at low x . The extracted longitudinal structure functions were in line with the data from the H1 Collaboration [Andreev et al . (H1 Collaboration), Eur. Phys. J. C 74 , 2814 (2014)] and the CT18 parametrization method [Hou et al . Phys. Rev. D 103 , 014013 (2021)].