International Journal of Modern Physics A, ( ISI ), Year (2023-9)

Title : ( Proton structure functions at low x: The Fractal Distributions )

Authors: Samira Shoeibi Mohsenabadi , Shahin Atashbar Tehrani , Seyyedeh Fatemeh Taghavi shahri ,

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This paper presents a method for extracting the Parton Distribution Functions (PDFs) at small momentum fractions $\\\\\\\\\\\\\\\\textit{x}$ 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 $\\\\\\\\\\\\\\\\textit{x}$ below $x<0.01$. To this end, a simple parametrization for the unintegrated Parton Distribution Functions based on the \\\\\\\\\\\\\\\"Fractal\\\\\\\\\\\\\\\" approach is considered. These functions have self-similar behavior at low $\\\\\\\\\\\\\\\\textit{x}$ and $k_t^2$ for sea quarks and have self-similar behavior at low $ x$ for gluon distribution. By integration from these 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 $\\\\\\\\\\\\\\\\textit{x}$ experimental datasets on electron-proton ($e^-p$) and positron-proton ($e^+p$) for natural current (NC) interactions in DIS processes at HERA for the range of $1.2 < Q^2 < 500$ ($GeV^2$) and $x<0.01$ are included in this analysis. The uncertainty estimations in the present analysis are carried out using the standard ``Hessian\\\\\\\\\\\\\\\'\\\\\\\\\\\\\\\' method. Considering the overall value of $\\\\\\\\\\\\\\\\chi^2/{\\\\\\\\\\\\\\\\rm dof}$ 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-$\\\\\\\\\\\\\\\\textit{x}$ observable and recent parameterizations for the PDFs.


, Proton structure functions, low x, Fractal
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author = {سمیرا شعیبی محسن آبادی and شاهین آتشبار تهرانی and Taghavi Shahri, Seyyedeh Fatemeh},
title = {Proton structure functions at low x: The Fractal Distributions},
journal = {International Journal of Modern Physics A},
year = {2023},
month = {September},
issn = {0217-751X},
keywords = {Proton structure functions; low x; Fractal},


%0 Journal Article
%T Proton structure functions at low x: The Fractal Distributions
%A سمیرا شعیبی محسن آبادی
%A شاهین آتشبار تهرانی
%A Taghavi Shahri, Seyyedeh Fatemeh
%J International Journal of Modern Physics A
%@ 0217-751X
%D 2023