QCD evolution of the spin structure functions of the neutron and proton

Models of the long-distance behavior of QCD can be used to make predictions for the twist-two piece of the current correlation function appearing in deep-inelastic scattering. The connection between the model predictions, valid at a four-momentum transfer squared $Q^2$ of the order of 1 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, and the data, collected at much higher $Q^2$, is provided by perturbative QCD. We present here the details of a method, previously used for spin-averaged lepton scattering, applied to the spin-dependent case. We then use the method to make predictions for the spin structure functions $g_{\mathrm{l}}^{\mathrm{proton}}$ and $g_{\mathrm{l}}^{\mathrm{neutron}}$.