https://doi.org/10.1140/epja/s10050-025-01706-2
Regular Article - Theoretical Physics
Valence densities and Chebyshev polynomials: nonsinglet structure function up to 
LO accuracy and related sum rules
1
Physics Department, Shahid Bahonar University of Kerman, Kerman, Iran
2
Physics Department, Yazd University, Yazd, Iran
3
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran
4
Department of Physics, Faculty of Nano and Bio Science and Technology, Persian Gulf University, 75169, Bushehr, Iran
Received:
9
June
2025
Accepted:
25
September
2025
Published online:
13
October
2025
In this study, we investigate the extraction of the nonsinglet structure function, 
, where the valence input densities are parameterized in terms of the Chebyshev polynomials. These polynomials provide an efficient basis for approximating functions, and using them in the analysis of structure functions allows for a compact and accurate representation. We then construct the Mellin-transformed of structure function where the nuclear effect is imposed on the parameterized valence densities. The Chebyshev polynomial approach provides an effective framework for the analysis of the nonsinglet structure function , offering accurate and computationally efficient calculations. Using the Wilson coefficient and splitting functions available in the literature, the evolution of the moment of structure functions in Mellin space is done up to LO accuracy. Transforming the structure function in Mellin space to the x-Bjorken space, is performed taking into account the Jacobi polynomials expansions. We compare our results with the results of some models and also the available experimental data for iron target and obtain good agreement with these findings. To further support our QCD analysis on valence densities, we calculate various sum rules such as Gross-Llewellyn-Smith (GLS), Bjorken unpolarized (Bup) and Bjorken polarized (Bp) sum rules, as well as the Adler sum rule. Our results align well with both the theoretical predictions and the available experimental data and also verify the connection between three GLS, Bup, and Bp sum rules.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
