Comparative insights into gluon and proton structure through parton distribution functions

TL;DR

Problem: accurate understanding of proton structure via PDFs and their $Q^2$ evolution. Approach: compare CT14, MMHT2014, and NNPDF4.0 global PDF sets using APFEL to solve the DGLAP equations for $f_i(x,Q)$ starting from $Q_0 \sim 1$ GeV over broad $x$ and $Q$ and across LO, NLO, NNLO. Findings: gluon distributions dominate at small $x$, quark distributions dominate at large $x$, with predictable $Q$-dependence and inter-set differences visible in the plots; these trends align with DGLAP expectations. Significance: the work informs LHC cross-section predictions, validates QCD behavior across scales, and underscores the value of continual, data-driven PDF refinements and uncertainty quantification.

Abstract

Study of parton distribution functions (PDFs) has led to a finer cognisance of the structure of partons in hadrons and the proton structure functions in deep inelastic scattering (DIS). PDFs are instrumental in predicting results for most of the hard-scattering processes measured at the Large Hadron Collider (LHC). However, due to the non-perturbative nature of partons, calculation of parton distributions using perturbative QCD (Quantum Chromodynamics) cannot be done. The analysis of PDFs, therefore, needs a relentless effort. In this paper, we study a comparative approach of three global PDF sets, viz. CT14, MMHT2014 and NNPDF 4.0. Gluon distribution functions and proton structure functions have been evaluated in a wide range of momentum fraction \textit{x} and energy scale \textit{Q}; and plausible observations have been made.

Figures (7)

• Figure 1: Gluon distribution function versus momentum fraction x at fixed energy scales Q of 1.5, 3, 10, 50, 100 and 1000 GeV.
• Figure 2: Proton structure function versus momentum fraction x at fixed energy scales Q of 1.5, 3, 10, 50, 100 and 1000 GeV.
• Figure 3: Gluon distribution function versus energy scale Q at fixed x of values $10^{-2}, 10^{-3}, 10^{-4}, 10^{-5}, 0.2$ and $0.7$.
• Figure 4: Proton structure function versus energy scale Q at fixed x of values $10^{-2}, 10^{-3}, 10^{-4}, 10^{-5}, 0.2$ and $0.7$.
• Figure 5: CT14 LO, NLO and NNLO PDFs at different values of energy scale Q.