High $Q^2$ Behavior of the Proton Structure Function through the Balitsky-Kovchegov Equation

Numerous experimental and theoretical investigations have highlighted the power law behavior of the proton structure function $F_2(x, Q^2)$, particularly the dependence of its power constant on various kinematic variables. In this study, we analyze the proton structure function $F_2$ employing the analytical solution of the Balitsky-Kovchegov equation, with a focus on the high $Q^2$ regime and small $x$ domains. Our results indicate that as $Q^2$ increases, the slope parameter $\lambda$, which characterizes the growth rate of $F_2$, exhibits a gradual decrease, approaching a limiting value of $\lambda \approx 0.41 \pm 0.01$ for large $Q^2$. We suggest that this behavior of $\lambda$ may be attributed to mechanisms such as gluon overlap and the suppression of phase space growth. To substantiate these conclusions, further high-precision electron-ion collision experiments are required, encompassing a broad range of $Q^2$ and $x$.