A global reanalysis of nuclear parton distribution functions

TL;DR

This work delivers a global leading-order DGLAP reanalysis of nuclear parton distributions within the EKS98 framework, introducing automated χ^2 minimization and a Hessian-based uncertainty quantification for nPDFs. It achieves a good fit with 16 free parameters (χ^2/d.o.f. ≈ 0.82) and finds the old EKS98 parametrization remains fully compatible within uncertainties. The valence sector is comparatively well constrained, while gluon and sea-quark modifications remain poorly determined in several x-regimes, highlighting the need for more data, especially on gluons. The study also explores the potential for stronger gluon shadowing, noting that current DIS/DY data allow room for such variations but do not mandate them, and it points to future extensions to NLO analyses and inclusion of RHIC/LHC measurements.

Abstract

We determine the nuclear modifications of parton distribution functions of bound protons at scales $Q^2\ge 1.69$ GeV$^2$ and momentum fractions $10^{-5}\le x\le 1$ in a global analysis which utilizes nuclear hard process data, sum rules and leading-order DGLAP scale evolution. The main improvements over our earlier work {\em EKS98} are the automated $χ^2$ minimization, simplified and better controllable fit functions, and most importantly, the possibility for error estimates. The resulting 16-parameter fit to the N=514 datapoints is good, $χ^2/{\rm d.o.f}=0.82$. Within the error estimates obtained, the old {\em EKS98} parametrization is found to be fully consistent with the present analysis, with no essential difference in terms of $χ^2$ either. We also determine separate uncertainty bands for the nuclear gluon and sea quark modifications in the large-$x$ region where they are not stringently constrained by the available data. Comparison with other global analyses is shown and uncertainties demonstrated. Finally, we show that RHIC-BRAHMS data for inclusive hadron production in d+Au collisions lend support for a stronger gluon shadowing at $x<0.01$ and also that fairly large changes in the gluon modifications do not rapidly deteriorate the goodness of the overall fits, as long as the initial gluon modifications in the region $x\sim 0.02-0.04$ remain small.

Figures (14)

• Figure 1: Initial nuclear ratios $R_V^A(x,Q_0^2)$ (solid lines), $R_S^A(x,Q_0^2)$ (dotted lines), $R_G^A(x,Q_0^2)$ (dashed lines) and $R_{F_2}^A(x,Q_0^2)$ (dotted-dashed lines) for $A=12$, 40, 117 and 208 at $Q_0^2=1.69$ GeV$^2$.
• Figure 2: Scale evolution of nuclear modifications: the ratios $R_V^A(x,Q^2)$, $R_V^A(x,Q^2)$, $R_V^A(x,Q^2)$, and $R_{F_2}^A(x,Q^2)$ at scales $Q^2=1.69$, 100 and 10000 GeV$^2$ for $A=12$ and 208.
• Figure 3: The computed ratio $R_{F_2}^A(x,Q^2)$ vs. $R_{F_2}^{\mathrm C}(x,Q^2)$ compared with the NMC data Arneodo:1996rv. The open symbols are the data points with errors added in quadrature, the filled ones are the corresponding results from this analysis.
• Figure 4: Calculated $R_{F_2}^A(x,Q^2)$ (filled symbols) are compared to SLAC (triangles) Gomez:1993ri, E665 (diamonds) Adams:1995is, NMC 95 (squares) Arneodo:1995cs and reanalysed NMC 95 (circles) data Amaudruz:1995tq. The asterisks denote our results calculated at the initial scale $Q_0^2$, these are for the smallest-$x$ data points whose scales lie in the region $Q^2<Q_0^2$.
• Figure 5: Top: The ratios $R_{F_2}^{\mathrm{Pb}}/R_{F_2}^{\mathrm D}$ from the E665 experiment (open triangles) Adams:1995is compared with the results from the present analysis (filled triangles). Bottom: Comparison of the ratios $R_{F_2}^{\mathrm{Pb}}/R_{F_2}^{\mathrm C}$. The NMC data Arneodo:1996rv are shown by open squares, the ratios calculated from the E665 data Adams:1995is by open triangles. For the error estimates in the latter case, see the text. The corresponding theoretical results are again shown by the filled symbols, and by asterisks if the experimental $Q^2$ is below our initial scale $Q^2_0$.