Proton structure functions at low x: The fractal distributions.

This paper presents a method for extracting the parton distribution functions (PDFs) at small momentum fractions x and at the next-to-leading order (NLO) accuracy in perturbative quantum chromodynamics. It turns out that the PDFs can be described by the "Fractal" or self-similar distributions at low x below x < 0. 0 1. To this end, a simple parametrization for the unintegrated PDFs based on the "Fractal" approach is considered. These functions have self-similar behavior at low x and k t 2 for sea quarks and have self-similar behavior at low x for gluon distribution. By integration from these transverse momentum distributions (TMDs), the initial input densities are obtained and the model's free parameters are then calculated using the experimental data released by the HERA experiment. The small- x experimental datasets on electron–proton ( e − p) and positron–proton ( e + p) for natural current (NC) interactions in deep inelastic scattering (DIS) processes at HERA for the range of 1. 2 < Q 2 < 5 0 0 (GeV2) and x < 0. 0 1 are included in this analysis. The uncertainty estimations in this analysis are carried out using the standard "Hessian" method. Considering the overall value of χ 2 ∕ dof and theory-to-data comparisons, the results indicate good agreements between the experimental datasets and the theoretical predictions. A detailed comparison is also presented between the model's predictions for the relevant small- x observable and recent parametrizations for the PDFs. [ABSTRACT FROM AUTHOR]