Longitudinal Structure Function at the Limit $x=Q^2/s$

TL;DR

This paper investigates the longitudinal structure function at the minimal x value using the color dipole model and expansion method, confirming consistency with experimental data and exploring nonlinear effects at low x and Q^2.

Contribution

It introduces a next-to-leading order analysis of the longitudinal structure function at the limit x=Q^2/s, including nonlinear corrections for nuclear targets.

Findings

Results agree with HERA data

Longitudinal structure function is small at low Q^2

Nonlinear corrections are significant at low x and Q^2

Abstract

The longitudinal structure function for nucleons and nuclei is considered at fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$. 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 $F_{L}$ at $x=Q^2/s$ [Frank E.Taylor, Phys. Rev. D {\bf111}, 052001 (2025)] at moderate and large $Q^2$ values. The results, consistent with the dipole picture at low $Q^2$ 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 $Q^2$ are also considered. These results may enhance the deep inelastic scattering neutral current data in future colliders at low $x$ and low $Q^2$. The longitudinal structure functions for deuterium at low four-momentum transfer squared, $Q^2<1~\mathrm{GeV}^2$ at the LO and NLO approximations are determined and compared with the JLab E00-002 data.