[Paper Review] Nuclear parton distributions in the DGLAP approach

K. Eskola, H. Honkanen+3 more|ArXiv.org|Oct 26, 2001

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper evaluates nuclear parton distribution (nPDF) parametrizations within the DGLAP framework, comparing the EKS98, HIJING, and Hard Probe Collaboration (HPC) models against deep in-line lepton-nucleus scattering and Drell-Yan data. It finds that the HIJING parametrization overestimates nuclear shadowing and underestimates baryon number and momentum sum rules, while HPC performs better but still lacks scale and flavor dependence, with EKS98 offering the most consistent DGLAP-based nPDFs constrained by data and theoretical consistency.

ABSTRACT

Determination of the nuclear parton distributions within the framework of perturbative QCD, the DGLAP equations in particular, is discussed. Scale and flavour dependent nuclear effects in the parton distributions are compared with the scale and flavour independent parametrizations of HIJING and of the Hard Probe Collaboration. A comparison with the data from deep inelastic lepton-nucleus scattering and the Drell-Yan process in proton-nucleus collisions is shown.

Motivation & Objective

• To assess the consistency of widely used nPDF parametrizations—EKS98, HIJING, and HPC—within the DGLAP evolution framework.
• To evaluate how well these parametrizations reproduce experimental data from deep inelastic scattering (DIS) and Drell-Yan processes in proton-nucleus collisions.
• To identify shortcomings in existing parametrizations, particularly in their treatment of scale and flavor dependence, baryon number conservation, and momentum sum rules.
• To recommend improvements in fitting procedures and future extensions, such as next-to-leading order analysis and inclusion of higher-twist or saturation effects.

Proposed method

• Uses the DGLAP evolution equations to describe the scale evolution of nuclear parton distributions (nPDFs), ensuring consistency with perturbative QCD.
• Compares the EKS98 nPDF parametrization—derived from global fits to DIS and Drell-Yan data—with the scale- and flavor-independent HIJING and HPC parametrizations.
• Analyzes the ratio $ R_{F_2}^A(x,Q^2) = F_2^A / F_2^D $ from NMC data to test nuclear effects across different nuclei and $ x $-regions.
• Applies momentum sum rules and baryon number conservation to constrain the behavior of valence quarks, sea quarks, and gluons in the nPDFs.
• Evaluates the $ Q^2 $-dependence of $ F_2^{\text{Sn}}/F_2^{\text{C}} $ to constrain gluon distributions, as suggested in earlier work.
• Identifies that scale-independent parametrizations cannot reproduce the observed $ Q^2 $-dependence in $ F_2^{\text{Sn}}/F_2^{\text{C}} $, necessitating scale-dependent fits.

Experimental results

Research questions

• RQ1 How do the HIJING and HPC parametrizations of nuclear effects compare with experimental data from deep inelastic scattering and Drell-Yan processes?
• RQ2 To what extent do the HIJING and HPC models violate baryon number and momentum sum rules in heavy nuclei like $ ^{208}\text{Pb} $?
• RQ3 Can scale-independent parametrizations accurately describe the $ Q^2 $-dependence of the $ F_2^{\text{Sn}}/F_2^{\text{C}} $ ratio observed in NMC data?
• RQ4 Why is the EKS98 parametrization considered more reliable than HIJING or HPC in the DGLAP framework?
• RQ5 What improvements are needed in the DGLAP-based fitting procedure to better constrain uncertainties and include higher-order effects?

Key findings

• The HIJING parametrization overestimates the $ A $-dependence of nuclear shadowing and contradicts data, particularly in the $ x \lesssim 0.1 $ region.
• The HIJING model underestimates baryon number conservation by 18–24% for $ ^{208}\text{Pb} $ at $ Q^2 = 2.25\text{–}10^4 \, \text{GeV}^2 $, indicating a fundamental inconsistency.
• The HPC parametrization underestimates baryon number by 5–12% for $ ^{208}\text{Pb} $, though it performs better than HIJING in reproducing $ R_{F_2}^A $ ratios.
• The EKS98 parametrization, derived from DGLAP fits to data, satisfies momentum sum rules and is consistent with the $ Q^2 $-dependence of $ F_2^{\text{Sn}}/F_2^{\text{C}} $, indicating robustness.
• Scale-independent parametrizations cannot reproduce the observed $ Q^2 $-dependence of $ F_2^{\text{Sn}}/F_2^{\text{C}} $, which constrains gluon distributions and necessitates scale-dependent fits.
• The analysis rules out models where gluons exhibit stronger shadowing than quarks, as in Ansatz 2 of Ref. [4], due to inconsistency with data and momentum sum rules.