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.
Categories: hep-ph