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Nuclear parton distribution functions and their uncertainties

M. Hirai, S. Kumano, T. -H. Nagai

TL;DR

This work extends nuclear parton distribution analyses by incorporating F2 ratios, Drell–Yan data, and charm-quark effects, and by quantifying uncertainties with the Hessian method. NPDFs are parametrized as nucleon PDFs modified by weight functions, with the initial scale set to $Q_0^2=1\ \mathrm{GeV}^2$ and evolution via LO DGLAP; uncertainties are derived from the Hessian of the $\chi^2$ fit. The results show that valence quarks are relatively well constrained for moderate to large $x$, antiquarks are well determined for $x\lesssim0.1$ but poorly known at larger $x$, and gluons remain poorly constrained across all $x$, underscoring the need for more precise scaling-violation data. A practical code is provided to compute NPDFs for given $x$ and $Q^2$, facilitating their use in high-energy nuclear physics and neutrino-nucleus cross-section calculations. The findings have important implications for interpreting heavy-ion collisions and neutrino experiments, and they point to future measurements (e.g., enhanced $Q^2$-dependence data, neutrino facilities) to tighten gluon and medium-to-large-$x$ modifications.

Abstract

We analyze experimental data of nuclear structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross section ratios for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Valence-quark distributions are determined by the F_2 data at large x; however, the small-x part is not obvious from the data. On the other hand, the antiquark distributions are determined well at x~0.01 from the F_2 data and at x~0.1 by the Drell-Yan data; however, the large-x behavior is not clear. Gluon distributions cannot be fixed by the present data and they have large uncertainties in the whole x region. Parametrization results are shown in comparison with the data. We provide a useful code for calculating nuclear PDFs at given x and Q^2.

Nuclear parton distribution functions and their uncertainties

TL;DR

This work extends nuclear parton distribution analyses by incorporating F2 ratios, Drell–Yan data, and charm-quark effects, and by quantifying uncertainties with the Hessian method. NPDFs are parametrized as nucleon PDFs modified by weight functions, with the initial scale set to and evolution via LO DGLAP; uncertainties are derived from the Hessian of the fit. The results show that valence quarks are relatively well constrained for moderate to large , antiquarks are well determined for but poorly known at larger , and gluons remain poorly constrained across all , underscoring the need for more precise scaling-violation data. A practical code is provided to compute NPDFs for given and , facilitating their use in high-energy nuclear physics and neutrino-nucleus cross-section calculations. The findings have important implications for interpreting heavy-ion collisions and neutrino experiments, and they point to future measurements (e.g., enhanced -dependence data, neutrino facilities) to tighten gluon and medium-to-large- modifications.

Abstract

We analyze experimental data of nuclear structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross section ratios for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Valence-quark distributions are determined by the F_2 data at large x; however, the small-x part is not obvious from the data. On the other hand, the antiquark distributions are determined well at x~0.01 from the F_2 data and at x~0.1 by the Drell-Yan data; however, the large-x behavior is not clear. Gluon distributions cannot be fixed by the present data and they have large uncertainties in the whole x region. Parametrization results are shown in comparison with the data. We provide a useful code for calculating nuclear PDFs at given x and Q^2.

Paper Structure

This paper contains 13 sections, 7 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Analysis method
  3. Parametrization
  4. Charm-quark distributions
  5. Experimental data
  6. $\chi^2$ analysis
  7. Uncertainty of nuclear PDFs
  8. Comparison with $x$-dependent data
  9. Comparison with $Q^2$-dependent data
  10. Optimum parton distribution functions
  11. Summary
  12. Nuclear dependent parameters
  13. Practical code for calculating nuclear PDFs

Figures (10)

  • Figure 1: (Color online) Kinematical range is shown by $x$ and $Q^2$ values of the used data.
  • Figure 2: (Color online) Comparison with experimental ratios $R=F_2^A/F_2^D$. The ordinate indicates the fractional differences between experimental data and theoretical values: $(R^{exp}-R^{theo})/R^{theo}$.
  • Figure 3: (Color online) Comparison with experimental data of $R=F_2^A/F_2^{C,Li}$. The ratios $(R^{exp}-R^{theo})/R^{theo}$ are shown.
  • Figure 4: (Color online) Comparison with Drell-Yan data of $R=\sigma_{DY}^{pA}/\sigma_{DY}^{pA'}$. The ratios $(R^{exp}-R^{theo})/R^{theo}$ are shown.
  • Figure 5: (Color online) Parametrization results are compared with the data of $F_2$ ratios $F_2^{Ca}/F_2^{D}$ and Drell-Yan ratios $\sigma_{DY}^{pCa}/\sigma_{DY}^{pD}$. The theoretical curves and uncertainties are calculated at $Q^2$=5 GeV$^2$ for the $F_2$ ratios and at $Q^2$=50 GeV$^2$ for the Drell-Yan ratios.
  • ...and 5 more figures