Small-x behavior of non-singlet spin structure function and Bjorken sum rule with pQCD correction up to NNLO and Higher twist correction

Abstract: A calculation of the non-singlet part of spin dependent structure function, $xg_1^{NS}(x,Q^2)$ and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with $Q^2$ dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-$x$ for $xg_1^{NS}(x,Q^2)$ and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of $xg_1^{NS}(x,Q^2)$ and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.