Nonsinglet polarized nucleon structure function in infrared-safe QCD

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 the fractional analytical perturbation theory. Consequently, it is possible to remove the Landau singularities of the renormalized coupling, i.e., at the scales Q similar to Lambda, using this approach. This provides an opportunity to continue the desired calculations toward small values of energy scales even less than the Lambda scale. To modify the analytical perturbation theory, a newer approach is introduced, called 2 delta anQCD, in which the spectral function of the holomorphic coupling is parameterized in the low-energy 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 2 delta anQCD 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 2 delta anQCD 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 (BSR), using the 2 delta anQCD model. There is a good agreement between the available experimental data for the BSR and the results from the utilized model, especially at low-energy scales.