Color dipole cross section in the DGLAP improved saturation model

Abstract

We show that the geometric scaling of the dipole cross section can be explained using standard DGLAP perturbative evolution. The DGLAP-improved saturation model due to the Laplace transform method is considered at LO and NNLO approximations from the experimental data by relying on a Froissart-bounded parametrization of $$F_{2}(x,Q^{2})$$ F 2 ( x , Q 2 ) . These results are comparable with the Golec-Biernat–W$$\ddot{\mathrm {u}}$$ u ¨ sthoff (GBW) model in a wide kinematic region $$rQ_{s}$$ r Q s which takes into account charm mass. The successful description of $${\sigma }_{\mathrm {dip}}(x,r)/\sigma _{0}$$ σ dip ( x , r ) / σ 0 and $${\sigma }_{\mathrm {dip}}(rQ_{s})/\sigma _{0}$$ σ dip ( r Q s ) / σ 0 are presented.