Investigation of the ratio $\frac{{\sigma }_r}{F_2}(Q^2/s,Q^2)$ in the momentum-space approach

Abstract

We present a calculation of the ratio $\frac{{\sigma }_r}{F_2}(x,Q^2)$ in momentum-space approach using the Block-Durand-Ha (BDH) parameterization of the proton structure function $F_2(x,Q^2)$. The results are compared with H1 data and extended to high inelasticity. We also examine the ratio $\frac{{\sigma }_r}{F_2}(\frac{Q^2}{s},Q^2)$ obtained at a fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$, comparing them with both the HERA data and the color dipole model bounds. These results and comparisons with HERA data demonstrate that the suggested method for the ratio $\frac{{\sigma }_r}{F_2}$ can be applied in analyses of the Large Hadron Collider and Future Circular Collider projects. The effect of adding a simple higher twist term of the form $F_2\ast H_2/Q^2$ to the description of the ratio $\frac{{\sigma }_r}{F_2}(\frac{Q^2}{s},Q^2)$ at low-$x$ and low-$Q^2$ values for comparison with the color dipole bounds and the HERA data is investigated.