Photoabsorption cross section in the low-$x$ and low-$Q^2$ domain, and DGLAP evolution

The behavior of the gluon distribution of the proton in the low-$x$, low-$Q^2$ domain of deep inelastic electron-proton scattering (DIS) is being investigated. By considering two-gluon exchange as the dominant interaction in the low-$x$, low-$Q^2$ domain, we imply the well-known result of scaling of the photoabsorption cross section in terms of the scaling variable $\eta(W^2,Q^2)$. From this, we derive a reliable result for the gluon distribution at the leading order of the perturbative QCD improved parton model, based on evolution from a starting scale of $Q_0^2\cong 2$ GeV$^2$. The validity of evolution, when considering its quantitative modification at low-$Q^2$ without any alteration at larger values of $Q^2$, leads to a quantitative improvement in the extraction of the gluon distribution based on evolution from a starting scale of $Q^2$ conventionally chosen as $Q^2= Q_0^2\cong 2$ GeV$^2$.