Nonlinear corrections to the nuclear heavy flavor structure functions

TL;DR

The paper investigates nonlinear corrections to nuclear gluon and heavy-quark structure functions at small $x$ by numerically solving the GLR-MQ-ZRS evolution equation for $G^A(x,Q^2)$. It extends the collinear high-energy DAS framework to nuclei, computing $F_2^{c\bar c-A}$ and $F_L^{c\bar c-A}$ via convolution with nonlinear gluon distributions and includes LO/NLO coefficient functions, with results benchmarked against $nCTEQ15$, RGK, and H1/ZEUS data. Key findings show nonlinear recombination effects become significant at $x\lesssim 10^{-4}$ and low $Q^2$, growing with the nucleus size $A$ and depending on the correlation length $R$, while remaining compatible with existing nuclear PDF analyses and providing robust predictions for LHeC/EIC kinematics. The work advances saturation phenomenology in nuclei, informs global nPDF fits, and offers concrete predictions for future electron-ion collider measurements where nonlinear QCD dynamics are expected to be most pronounced.

Abstract

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.

Figures (8)

• Figure 1: Ratios between the PDFs evolved using the nonlinear (Eq.\ref{['GLR-MQ-ZRS2']}) and linear (Eq.\ref{['GA']}) evolution equations at $Q_0 = 2~\text{GeV}$ are shown as functions of $x$ for different values of $R$. The left, middle, and right plots correspond to $A = 1$, $12$, and $208$, respectively.
• Figure 2: The linear and nonlinear gluon distribution function for the nucleus of Au-197. Left panel: gluon distributions per nucleon and $R_{G}$ ratio ($R_G=\frac{G^A_{\rm GLR-MQ-ZRS}}{G^A_{\rm GLR-MQ}}$) as a function of $x$ for $Q^2 = 100\, \text{GeV}^2$. Right panel: linear gluon distribution function as a function of $x$ at $Q^2 = 100\, \text{GeV}^2$. Results are compared with the nuclear PDF set nCTEQ15 nCTEQ15 and the RGK method Guzey1 at the corresponding $Q^2$.
• Figure 3: The $Q^2$( ${5}{\text{GeV}^2} \leq Q^2 \leq {100}{\text{GeV}^2}$) evolution of $G(x,Q^2)$ for fixed values of the Bjorken-$x$. The correlation radius $R$ is taken to be $2$, $5$, and $6.34\, \text{GeV}^{-1}$. The left column shows the gluon distribution function for a nucleon ($A=1$) at $x=10^{-5}$ and $x=10^{-3}$, while the right side shows the corresponding distributions for a heavy nucleus ($A=208$) at the same $x$ values.
• Figure 4: The gluon nuclear modification factors $R_g^A=\frac{ G^A_{NL}}{A G^N_L}$ are calculated at NLO for various nuclei ( $\text{C}-12$ , $\text{Fe}-56$, $\text{Ag}-108$ and $\text{Pb}-208$) at $Q^2 =5\, \text{GeV}^2$ and $Q^2 =10 \, \text{GeV}^2$ with $R =5\, \text{GeV}^{-1}$, $R =6.34\, \text{GeV}^{-1}$
• Figure 5: The theoretical prediction for the linear and nonlinear structure function $F^{c\bar{c}}_2 (x, Q^2 )$ at LHeC center-of-mass energy($\sqrt{s} = 1.3\, \text{TeV}$) with $\mu^2 = Q^2 + 4m^2_c$ as a function of variable $Q^2$ for three different values of $W$, viz. $60$, $95$, and $140$, respectively. Experimental data are taken from the H1 H1-2005H1-2010 and ZEUS ZEUS2014ZEUS-2001 Collaborations as accompanied by total errors.