Abstract
We present nonlinear corrections (NLCs) 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 nonlinear 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). Comparisons between the nonlinear results with the bounds in the color dipole model (CDM) and HERA data indicate the consistency of the nonlinear behavior of the gluon distribution function at low x and low Q^{2}. The nonlinear longitudinal structure functions are comparable with the H1 Collaboration data in a wide range of Q^{2} values. Consequently, the nonlinear 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.
Highlights
Introduction[19,20,21,22]
The CT global analyses [8] explored a broad range of parametric forms for the parton distribution functions at the starting scale, Q = Q0
We have studied the effects of adding the nonlinear corrections to the distribution functions for transition from the linear to nonlinear regions
Summary
[19,20,21,22] In this region, gluon recombination terms, which lead to nonlinear corrections to the evolution equations, can become significant. The gluon recombination effects tame the growth of the gluon density towards low x These effects induce nonlinear power corrections to the DGLAP equations. The authors have considered deeply inelastic scattering at very high energies in the saturation regime and have developed a formalism which allows successive evaluation of the nonlinearities in the generalized evolution equation for the dipole densities. In the small-x region, the saturation scale Q2s (x) (Q2s = Q20(x/x0)−λ where Q0 and x0 are free parameters) indicates the saturation limit where the DGLAP and GLR-MQ terms in the nonlinear equation become equal and is usually defined as [13,14,52]. We summarize our main conclusions and remarks
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