Non-linear corrections to the derivative of nuclear reduced cross-section at small $x$ at a future electron-ion collider

TL;DR

The paper investigates non-linear corrections to nuclear parton distributions at small $x$ within the GLR–MQ framework using HIJING inputs, aiming to constrain these effects with inclusive observables at future electron–ion colliders. It formulates the nonlinear GLR–MQ modifications to DGLAP evolution, with a nonlinear term that scales as $[xg^{A}(x,Q^{2})]^{2}$, and proposes a derivative method on the nuclear reduced cross section $\sigma_{r}^{A}$ to access these corrections. Numerical results for $\mathrm{^{12}C}$ and $\mathrm{^{208}Pb}$ at $\mathcal{R}_{A}=1.25A^{1/3}$ fm show sizable nonlinear contributions to $\frac{1}{A}\frac{\partial}{\partial \ln Q^{2}}\Delta F_{2}^{A}(x,Q^{2})$ at small $x$ and low $Q^{2}$, in line with nPDFs like nCTEQ15, and reveal a scaling $\frac{1}{A}\frac{\partial}{\partial \ln Q^{2}}\Delta F_{2}^{A} \propto A(R_{g}^{A})^{2}\frac{\mathcal{R}^{2}}{\mathcal{R}_{A}^{2}}$. The study suggests that inclusive observables at the EIC can tightly constrain nonlinear shadowing and thereby inform saturation/CGC dynamics in nuclei.

Abstract

The determination of non-linear corrections to the nuclear distribution functions due to the HIJING parametrization within the framework of perturbative QCD, specifically the GLR-MQ equations, is discussed. We analyze the possibility of constraining the non-linear corrections present in distribution functions using the inclusive observables that will be measured in future electron-ion colliders (EIC and EICc). The results show that non-linear corrections play an important role in heavy nuclear reduced cross sections at low $x$ and low $Q^2$ values. We find that the non-linear corrections provide the correct behavior of the extracted nuclear cross sections and that our results align with data from the nCETQ15 parametrization group. We are currently discussing a satisfactory description of the non-linear corrections to the shadowing effect at small $x$.

Figures (6)

• Figure 1: The non-linear corrections to $\frac{1}{A}\frac{\partial}{\partial{\ln}Q^2}{\Delta}F_{2}^{A}(x,Q^2)$ for the heavy nucleus of Pb-208 are shown as a function of the momentum fraction $x$ at $Q^2=5~\mathrm{GeV}^2$ at $\mathcal{R}_{A}=1.25A^{1/3}~\mathrm{fm}$. These results are determined by the DL (square-purple) [30] and Block et al (circle-brown) [31-32] gluon distributions and compared with the nCETQ15 parametrization [33] results at $\mathcal{R}=2~\mathrm{GeV}^{-1}$ (solid curve-red), $\mathcal{R}=5~\mathrm{GeV}^{-1}$ (dashed curve- blue ) and $\mathcal{R}=1.25A^{1/3}~\mathrm{fm}$ (dashed- dot curve- black) with uncertainties.
• Figure 2: The same as Fig.1 for Pb-208 at $Q^2=10~\mathrm{GeV}^2$.
• Figure 3: Results of $\frac{1}{A}\frac{{\partial}}{{\partial}{\ln}Q^2}\Delta\sigma_{r}^A(x,Q^2)$ are shown as a function of $Q^2$ at $y=0.2$ (left) and $y=0.6$ (right) for the light nucleus of C-12 (black-solid curve) and the heavy nucleus of Pb-208 (red-dashed curve) due to the DL method [30].
• Figure 4: The same as Fig.3 due to the Block et al., method [31-32].
• Figure 5: Results of $\frac{1}{A}\Delta\sigma_{r}^A(x,Q^2)$ are shown as a function of $Q^2$ at $Q^2=5~\mathrm{GeV}^2$ (left) and $Q^2=5~\mathrm{GeV}^2$ (right) for the light nucleus of C-12 (black-square points) and the heavy nucleus of Pb-208 (red-circle points) due to the DL method [30].