Self-Similar Properties of the Proton Structure at Low x within the $\mathbf{\text{xFitter}}$ framework

The structure of the proton exhibits Fractal behavior at low $\mathit{\text{x}}$, where $\mathit{\text{x}}$ is the fraction of the proton’s momentum carried by the interacting partons. This Fractal behavior is characterized by self-similar properties at different scales and can be quantified using the concept of Fractal dimension. An investigation into the Fractal properties of the proton structure at low $\mathit{\text{x}}$ is critical for understanding the fundamental properties of the strong force and developing a more comprehensive understanding of the hadron structure. Fractals, characterized by self-similar patterns across scales, demonstrate a direct correlation between their Fractal dimension and entropy, where higher Fractal dimensions correspond to increased informational content. Furthermore, it is essential for designing high-energy physics experiments and developing more accurate models of subatomic particle interactions. This paper has a fresh look at the self-similar properties of the proton structure at low $\mathit{\text{x}}$. Our study involves the use of the $\mathbf{\text{xFitter}}$ framework to parameterize the proton structure functions with a Fractal formalism at low $\mathit{\text{x}}$. We also examine how the inclusion of new data affects the results of our analysis.