Perturbative and nonperturbative QCD corrections in polarized nucleon structure functions and spin asymmetries of nucleons

We have studied the deep inelastic scattering (DIS) of polarized charged leptons from polarized nucleon targets and evaluated the polarized nucleon structure functions $g_{1N,2N}(x,Q^2)$ as well as the nucleon asymmetries $A_{1N,2N}(x,Q^2)$ for protons and neutrons. The higher order perturbative corrections up to the Next-to-Next-to-the-Leading Order (NNLO), using the parameterization of Polarized Parton Distribution Functions (PPDFs) given by Borsa, Stratmann, Vogelsang, de Florian and Sassot (BDSSV24) in the 3-flavor $\overline{\textrm{MS}}$ scheme, along with the nonperturbative corrections$-$namely the twist-3 corrections and the Target Mass Corrections (TMC)$-$have been included in the calculations. The numerical results for the polarized nucleon structure functions, the nucleon asymmetries and the sum rule integrals of the nucleon structure functions$-$corresponding to the Ellis-Jaffe, Bjorken, and Burkhardt-Cottingham sum rules$-$have been evaluated numerically and are found to be in agreement with the experimental results from SLAC, CERN, DESY and JLab. The benchmarking of the PPDFs of BDSSV24 at NNLO using the present data on polarized nucleon structure functions and other observables will be useful in studying the nuclear medium effects in the scattering of the charged leptons from nuclei at the JLab, EIC, DESY, etc., and the scattering of the (anti)neutrinos from polarized nucleons and nuclei at the proposed neutrino factories.