Nonlinear corrections to the nuclear heavy flavor structure functions

We study numerically the small-$x$ behavior of the nuclear gluon distribution function ${G}^{A}(x,{Q}^{2})$ in the next-to-leading order (NLO) approximation of the Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) nonlinear equation and quantify the impact of gluon recombination in the kinematic range $x\ensuremath{\le}{10}^{\ensuremath{-}2}$ and ${Q}^{2}\ensuremath{\ge}5\phantom{\rule{0.28em}{0ex}}{\text{GeV}}^{2}$. The results are comparable to the Rausch-Guzey-Klasen (RGK) [J. Rausch, V. Guzey, and M. Klasen, Phys. Rev. D 107, 054003 (2023)] nuclear gluon distributions and the nCTEQ15 parametrization at the corresponding ${Q}^{2}$ values. Using the solutions of ${G}^{A}(x,{Q}^{2})$ in the framework of the nonlinear GLR-MQ-ZRS evolution equation, both the linear and nonlinear behaviors of the charm structure functions of nuclei per nucleon, ${F}_{2}^{c\overline{c}\ensuremath{-}A}(x,{Q}^{2})$ and ${F}_{L}^{c\overline{c}\ensuremath{-}A}(x,{Q}^{2})$, are considered. The results reveal that nonlinear corrections play an important role in the charm nuclear reduced cross sections at small $x$ and low ${Q}^{2}$ values. The computed results are compared with experimental data from the H1 and ZEUS Collaborations.