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

Abstract

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 $.