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.