One-to-One correspondence of soft and hard Pomeron with the CDP of the gluon density at low $x$

Abstract: The correspondence between the gluon density behavior of the color dipole picture and the two-Pomeron approach at low $x$ deep inelastic scattering is considered. For photon virtualities of $Q^{2}{\gtrsim}10~\mathrm{GeV}^{2}$, the results for the parametrization and CDP models are defined by the CDP asymptotic limit and are compatible with the soft and hard-Pomeron approach. These results show that the hard-Pomeron trajectory does not guarantee converging towards the asymptotic representation at low and large $Q^{2}$ ($Q^{2}{\lesssim}100~\mathrm{GeV}^{2}$) values in a wide range of the virtual-photon-proton energy squared. The gluon distributions can be obtained directly in terms of the proton structure functions and the running coupling and compared with the results from the GJR and MSTW parametrizations.