Scale evolution of nuclear parton distributions

TL;DR

Problem: Nuclear PDFs and their scale evolution at small $x$. Approach: determine initial nuclear PDFs at $Q_0^2$ from DIS and DY data with sum-rule constraints, then evolve using LO DGLAP; Findings: LO DGLAP evolution reproduces the $Q^2$-dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ observed by NMC, supporting negligible GLRMQ corrections in the studied range; Gluon shadowing is constrained but not tightly; The method provides a model-independent framework for nuclear PDFs and supports using leading-twist QCD for nuclear effects. Significance: offers a path to integrate nuclear modifications into global PDF analyses and to improve predictions for nuclear collisions.

Abstract

Using the NMC and E665 nuclear structure function ratios $F_2^A/F_2^D$ and $F_2^A/F_2^{C}$ from deep inelastic lepton-nucleus collisions, and the E772 Drell--Yan dilepton cross sections from proton-nucleus collisions, and incorporating baryon number and momentum sum rules, we determine nuclear parton distributions at an initial scale $Q_0^2$. With these distributions, we study QCD scale evolution of nuclear parton densities. The emphasis is on small values of $x$, especially on scale dependence of nuclear shadowing. As the main result, we show that a consistent picture can be obtained within the leading twist DGLAP evolution, and in particular, that the calculated $Q^2$ dependence of $F_2^{Sn}/F_2^{C}$ agrees very well with the recent NMC data.

Figures (10)

• Figure 1: Typical correlation of the scale $\langle Q^2\rangle$ and $x$ in measurements of $F_2^A(x,Q^2)$ in deeply inelastic $lA$ scatterings and correlation of the invariant mass $\langle Q^2\rangle$ and $x=x_2$ of Drell-Yan cross sections measured in $pA$ collisions. The correlations in some of the NMC data NMCre (solid lines), NMCsys (dotted-dashed), NMCsat (dotted) and in some of the E665 data E665sat (dashed), and in the E772 data E772PMcG (long dashed) are shown. The horizontal dotted line illustrates the initial scale $Q_0^2$ we have chosen and above which we perform the DGLAP evolution of nuclear parton densities.
• Figure 2: The initial nuclear ratios $R_G^A(x,Q_0^2)$ (solid line), $R_V^A(x,Q_0^2)$ (dotted) and $R_S^A(x,Q_0^2)$ (dashed) for isoscalar nuclei at $Q_0^2=2.25$ GeV$^2$. The ratio $R_{F_2}^A(x,Q_0^2)$ (dotted-dashed) is also shown.
• Figure 3: Scale evolution of the ratios $R_G^A(x,Q^2)$, $R_S^A(x,Q^2)$, $R_V^A(x,Q^2)$ and $R_{F_2}^A(x,Q^2)$ for an isoscalar nucleus $A$=208. The ratios are shown as functions of $x$ at fixed values of $Q^2=$ 2.25 GeV$^2$ (solid lines), 5.39 GeV$^2$ (dotted), 14.7 GeV$^2$ (dashed), 39.9 GeV$^2$ (dotted-dashed), 108 GeV$^2$ (double-dashed), equidistant in $\log Q^2$, and 10000 GeV$^2$ (dashed). For $R_V^A$ only the first and last ones are shown.
• Figure 4: Scale evolution of the ratio $R_{F_2}^A(x,Q^2)$ for isoscalar nuclei $A$=4, 12 and 40. As in Fig. \ref{['RQ2']}, the ratios are plotted as functions of $x$ but with $Q^2$ fixed to 2.25, 3.70, 6.93, 12.9, 24.2 GeV$^2$, equidistant in $\log Q^2$, and 10000 GeV$^2$. The reanalyzed NMC data NMCre is shown by the boxes, the reanalyzed SLAC data by the triangles SLACre. The statistical and systematic errors have been added in quadrature. The filled circles show our calculation at the $\langle Q^2 \rangle$ values of the NMC data. Notice that the vertical scale of each panel is different.
• Figure 5: The ratio $R_{F_2}^{\rm C}(x,Q^2)$ shown together with the renanalyzed NMC data NMCre (boxes) and the combined NMC data NMCsat (triangles). The calculated $R_{F_2}^{\rm C}$ are shown at the same fixed values of $Q^2$ as in Fig. \ref{['RF2Q2']}. Notice that at $x<0.01$ the scales $\langle Q^2\rangle$ of the data are less than our $Q_0^2=2.25$ GeV$^2$. The statistical and systematic errors of the data are added in quadrature.