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

TL;DR

This paper investigates the high $Q^2$ behavior of the proton structure function $F_2$ using the Balitsky-Kovchegov equation, revealing a decreasing slope parameter $\\lambda$ that approaches approximately 0.41 at large $Q^2$, indicating saturation effects.

Contribution

It provides an analytical solution-based analysis of $F_2$ at high $Q^2$ and small $x$, highlighting the behavior of the growth rate parameter $\\lambda$ with implications for gluon saturation.

Findings

The slope parameter $\\lambda$ approaches 0.41 at high $Q^2$.

$\\lambda$ decreases gradually with increasing $Q^2$.

Gluon overlap and phase space suppression may explain the observed behavior.

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 $.