Nonlinear corrections on the parameterization methods

Abstract

We present non-linear corrections (NLC) to the distribution functions at low values of $x$ and $Q^2$ using the parametrization $F_2(x,Q^2)$ and $F_L(x,Q^2)$. We use a direct method to extract non-linear corrections to the ratio of structure functions and the reduced cross section in the next-to-next-to-leading order (NNLO) approximation with respect to the parametrization method (PM). Comparison between the non-linear results with the bounds in color dipole model (CDM) and HERA data indicate the consistency of the non-linear behavior of the gluon distribution function at low-$x$ and low-$Q^2$. The non-linear longitudinal structure functions are comparable with the H1 Collaboration data in a wide range of $Q^2$ values. Consequently, the non-linear corrections at NNLO approximation to the reduced cross sections at low and moderate $Q^2$ values show good agreement with the HERA combined data. These results at low $x$ and low $Q^2$ can be applied to the LHeC region for analyses of ultra-high-energy processes.

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