Usefulness of the covariant parton model as a complement to pQCD in extracting spin structure functions

As a complement to conventional perturbative quantum chromodynamics (pQCD) there is an approach that is called covariant parton model (CPM). As mentioned in related literature, this model is based on the intrinsic motion of quarks where a spherical symmetry is assumed for distribution of fermion momenta in three dimensions inside the nucleon. This model provides the exact spin value for the nucleon by assuming it contains only three valence quarks. This model also gives accurate numerical results for various QCD sum rules. Hence, it would be advantageous to analyze the spin structure functions of a nucleon in CPM. For this purpose we resort to the solution of the Dirac equation with a harmonic oscillator potential to yield us the bare quark densities. Following that utilizing the chiral quark model, the ${u}_{v}$ and ${d}_{v}$ valence quark densities can be determined at an initial energy scale. By achieving the required input and doing the evolution of valence densities, ${g}_{1}$ and ${g}_{2}$ spin nucleon structure functions can be extracted in CPM, demonstrating qualitative agreement with experimental findings. We also compute these structure functions through conventional pQCD at next-to-leading-order accuracy, which, in addition to the evolution of valence densities, necessitates the evolution of sea and gluon densities. The findings are similar to those from CPM, suggesting the effectiveness of CPM for conducting phenomenological analyses.