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 $Q \sim \Lambda$, 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 \textit{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.
Highlights
QCD analysis of deep-inelastic scattering (DIS) data provides us new insight into the hadron physics
The results show that the obtained nucleon structure function at small energy scales has smoother behavior when using the 2δanQCD model than the underlying perturbative QCD (pQCD)
II, we provide a brief discussion of the theoretical formalism for different aspects of analytic QCD (anQCD), including the 2δanQCD model
Summary
QCD analysis of deep-inelastic scattering (DIS) data provides us new insight into the hadron physics. The numerical values of structure functions are affected by the energy scale, at which the renormalized coupling constant as the perturbation expansion parameter is evaluated. The analysis of the structure functions should lead to consistent results with the related experimental data To achieve this aim, it is needed to model the parton densities, as ingredients of nucleon structure, at an initial energy scale. Some newer constructions of the coupling constant in analytic QCD (anQCD) are based on the modifications of the spectral function at low-energy scales.
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