Self-similar behavior of the Neutron Fracture Functions

In this article, we have employed fractal formalism to calculate the Fracture Functions of the Leading neutron produced in \textit{ep} collisions. The fractal concept describes the self-similar behavior of the proton structure at Leading neutron production of semi-inclusive Deep Inelastic Scattering at the low values of the fractional momentum variable $\beta$. The Fracture Functions (FFs) parameterized the non-perturbative part of the fragmentation process at the initial scale of Q$_{0}^{2}$. In this analysis, we benefit from the Leading neutron (Ln) experimental data published by H1 Collaboration and in order to estimate the uncertainty of neutron FFs and corresponding observables, we used the Hessian method. As a consequence of this Next-to-Leading order QCD analysis, we achieve a nice agreement between the prediction of our model for neutron FFs and experimental data. It seems that the fractal approach based on the self-similar behavior of these conditional parton distribution functions at low x can nicely describe the experimental data.