Nonlinear correction to the nuclear gluon distribution function

Abstract

In the present paper, we use the parameterization of the proton structure function to derive an analytical solution for the nuclear gluon density at small x. The behavior of nuclear parton distribution functions (nPDFs) in the next-to-leading-order (NLO) approximation at small x is defined numerically in a semi-analytical study using the Gribov–Levin–Ryskin and Mueller–Qiu (GLR-MQ) approach. We observe that the gluon distribution increases with increasing \(Q^2\), increasing atomic number A, and decreasing x. The results of the nonlinear GLR-MQ evolution equation are comparable to the Rausch–Guzey–Klasen (RGK) nuclear gluon distributions. The longitudinal structure function is considered according to the nonlinear effects of the gluon density behavior at small x. These results show that the nonlinear effects are important in \(F^A_L (x,Q^2\)) for heavy nuclei.