“School of Particles And Accelerator”
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Paper IPM / Particles And Accelerator / 15896  


Abstract:  
The polarized nucleon structure function in the nonsinglet case is investigated here by a new insight rather than conventional perturbative QCD (pQCD).
For this purpose we note that the solution of the evolution equations in moment space involves noninteger powers of the coupling constant. Therefore it is possible to employ a new approach which is called fractional analytical perturbation theory Consequently, it is possible to remove the Landau singularities of the renormalized coupling, i.e., at the scales Q ∼ Λ, using this approach. This provides
an opportunity to continue the desired calculations toward small values of energy scales even less than the Λ scale. To modify the analytical
perturbation theory, a newer approach is introduced, called 2δanQCD, in which the spectral function of the holomorphic coupling is
parameterized in the lowenergy region by two delta functions. This model gives us more reliable results for the considered QCD observables,
even in the deep infrared region. We calculate the nonsinglet part of the polarized nucleon structure function, using the 2δanQCD
model, and compare it with the result from the underlying pQCD where both are in a new defined scheme, called the Lambert scheme. For this purpose we employ the anQCD package in the Mathematica environment to
establish the analytic (holomorphic) coupling constant. The results at various energy scales are also compared with the available experimental data, and it
turns out that there is a good consistency between them. The results show that the obtained nucleon structure function at small energy scales has smoother
behavior when using the 2δanQCD model than the underlying pQCD. In fact the coupling constant in analytic QCD behaves moderately and it makes the result approach the available data in a better way.
We also consider the Q^{2} dependence of the Bjorken sum rule the (BSR), using the 2δanQCD model. There is a good agreement between the
available experimental data for BSR and the results from the utilized model, especially at lowenergy scales.
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