Low-x contribution to the Bjorken sum rule within unified $l{n}^{2}x+$LO DGLAP approximation

Abstract

The small-$x$ contributions to the Bjorken sum rule within unified picture $l{n}^{2}x+$LO DGLAP for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Theoretical predictions for ${\int }_0^{0.003}{g}_1^{NS}(x,Q^2=10)dx$ are compared with the SMC small-$x$ data. Rough estimation of the slope $\lambda$, controlling the small-$x$ behaviour of $g_1^{NS}\sim x^{-\lambda }$ from the obtained results and SMC data is performed. The crucial role of the running coupling ${\alpha }_s={\alpha }_s(Q^2/z)$ at low-$x$ is taken into account.

Comments: 15 pages, 3 eps figures