Reduced cross section and gluon distribution in a momentum-space approach

We present a calculation of the reduced cross section in momentum-space approach utilizing the Block-Durand-Ha (BDH) parameterization of the proton structure function $F_{2}(x,Q^2)$ and the leading-order (LO) longitudinal structure function $F_{L}(x,Q^2)$, proposed by Boroun and Ha [G.R. Boroun and P.Ha, Phys. Rev. D {\bf 109} (2024) 094037] using Laplace transform techniques. Our results are compared with the HERA data and extended to the Large Hadron electron Collider (LHeC) domain. We also examine the ratio $F_{L2}(x, Q^2)=F_{L}(x, Q^2)/F_{2}(x, Q^2)$ obtained from our work, comparing it with both the H1 data and the color dipole (CDP) bounds. We find that our results for the reduced cross section and the ratio $F_{L2}(x, Q^2)$ agree with the H1 data. Finally, our evaluation of the gluon distribution functions $G(x,Q^2)$ in momentum-space approach shows very good concordance with the NNPDF3.0LO gluon structure functions for moderate $Q^2$ in the range $10^{-5}{\leq}x{\leq}1$.