Longitudinal Structure Function at the Limit x=Q²/s

The longitudinal structure function for nucleons and nuclei is considered at fixed √s and Q² to the minimum value of x given by Q²/s. This is done using the expansion method and color dipole model in the next-to-leading order approximation. The extracted longitudinal structure functions were consistent with HERA hepdata [ https://www.hepdata.net/record/ins1377206] and the determination of FL at x=Q²/s [Frank E.Taylor, Phys. Rev. D {111}, 052001 (2025)] at moderate and large Q² values. The results, consistent with the dipole picture at low Q² values, show that the longitudinal structure function is small as expected due to the transverse polarization of the exchanged photon and the strong suppression of the dominant gluon component. Nonlinear corrections to the nuclear longitudinal structure function at low values of x and Q² are also considered. These results may enhace the deep inelastic scattering neutral current data in future colliders at low x and low Q².