Analytic derivation of the non-linear gluon distribution function

Abstract

In the present article, two analytical solutions based on the Laplace transforms method for the linear and non-linear gluon distribution functions have been presented at low values of $x$. These linear and non-linear methods are presented based on the solutions of the Dokshitzer-Gribov- Lipatov-Altarelli-Parisi (DGLAP) evolution equation and the Gribov-Levin-Ryskin Mueller-Qiu (GLR-MQ) equation at the leading-order accuracy in perturbative QCD respectively. The gluon distributions are obtained directly in terms of the parametrization of structure function $F_2(x,Q^2)$ and its derivative and compared with the results from the parametrization models. The $n_f$ changes at the threshold are considered in the numerical results. The effects of the non-linear corrections are visible as $Q^2$ decreases and vanish as $Q^2$ increases. The nonlinear corrections tame the behavior of the gluon distribution function at low $x$ and $Q^2$ in comparison with the parametrization models.

arXiv commentarXiv admin note: text overlap with arXiv:2109.08878

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