The color dipole model bounds with the gluon-gluon recombination correction

We present nonlinear (NL) and higher twist (HT) corrections to the color dipole model (CDM) bounds at low values of $x$ and $Q^{2}$ using the parameterization method. Consistency between the bounds at this region describe that a transition from the linear to the nonlinear behavior is dependence on the behavior of the gluon distribution function. The parameters in the color dipole model are comparable with the color dipole bounds at low values of $Q^{2}$. Consequently, the obtained reduced cross sections at low and moderate $Q^{2}$ values due to the NL+HT effects show a good agreement with the H1 data.