Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

Abstract

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions $\delta F^{\mathrm {S}}(x,Q^{2})=\mathcal {F}[\partial \delta F^{\mathrm {S}}_{0}(x), \delta F^{\mathrm {S}}_{0}(x)]$ and ${\delta G}(x,Q^{2})=\mathcal {G}[\partial \delta G_{0}(x), \delta G_{0}(x)]$ . We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC’08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.