Nonlinear corrections to the nuclear heavy flavor structure functions

We study numerically the small-$x$ behaviour of the nuclear gluon distribution function $G^A(x,Q^2)$ at 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 of $x \le 10^{-2}$ and $Q^2 \ge 5 \text{GeV}^2$ respectively. 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, the linear and nonlinear behavior of the charm structure functions of nuclei per nucleon $F^{c\bar{c}-A}_2(x,Q^2)$ and $F^{c\bar{c}-A}_L(x,Q^2)$ are considered. The results reveal that nonlinear corrections play an important role in 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.