“School of Particles”
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| Paper IPM / Particles / 18259 |
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Parton Distribution Functions (PDFs) are important quantities that describe the distributions of momentum and spin of partons inside a nucleon. Their exact determination is crucial for precision tests of the Standard Model and also for making predictions of experimental results in high energy colliders. Gegenbauer polynomials are a set of orthogonal polynomials which could be used to parameterize PDFs. These polynomials are solutions to a second-order differential equation and depend on the two parameters: the degree of polynomials and a constant known as the Gegenbauer coefficient. By fitting the experimental data with a combination of Gegenbauer polynomials, one can extract the values of unknown parameters including these coefficients, which in turn can provide a physical insight into the structure of proton. The use of Gegenbauer polynomials in PDFs has several advantages over other parameterizations; they have better convergence properties and can more accurately capture the shape of the PDFs at high momentum fractions. Through this work we use these polynomials to parameterize the polarized PDFs (PPDFs) where the positivity constraint enforced on them. In continuation from two analysis with and without considering the higher twist effects we determine the polarized structure functions of proton, neutron and deuteron at NLO accuracy. Considering all available data, specifically including final JLAB CLAS/EG1b data for proton and deuteron, we show that taking the higher twist effect is necessary to determination of the PPDFs. Investigation of the polarized Bjorken sum rule and proton helicity sum rule is also conducted to verify the fitting results. The findings show expected alignment with the existing data and certain parametrization models.
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