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

## TL;DR

This paper calculates the non-singlet spin structure function and the Bjorken sum rule up to NNLO with higher twist corrections using a combined Regge and pQCD approach, showing good agreement with experimental data.

## Contribution

It introduces a unified Regge-pQCD framework to solve DGLAP equations at small-x up to NNLO, including higher twist effects, and compares results with experimental data and other models.

## Key findings

- Results agree well with experimental data from multiple collaborations.
- Theoretical predictions of BSR are consistent with QCD expectations.
- Higher twist contributions are effectively parametrized and incorporated.

## 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.