Parton momentum and helicity distributions in the nucleon

TL;DR

The paper provides a comprehensive snapshot of the current status of spin-averaged and spin-dependent PDFs, detailing the QCD framework for global fits, the treatment of heavy-quark and nuclear effects, and the handling of power corrections and uncertainties. It synthesizes results from major global analyses to illustrate where PDFs are well constrained and where large uncertainties persist, particularly at large x and in the polarized sector. The discussion highlights how diverse data types (DIS, Drell–Yan, jet and boson production, SIDIS) and lattice QCD moments inform the flavor, spin, and gluon content of the nucleon, while outlining methodological tools (Hessian, Lagrange multiplier, Monte Carlo) used to quantify uncertainties. The outlook emphasizes upcoming facilities and theoretical advances that promise to tighten constraints, extend flavor separation (e.g., strange and CSV), and probe high-x dynamics and gluon polarization with greater precision.

Abstract

We review the current status of spin-averaged and spin-dependent parton distribution functions (PDFs) of the nucleon. After presenting the formalism used to fit PDFs in modern global data analyses, we discuss constraints placed on the PDFs by specific data types. We give representative examples of unpolarized and polarized PDFs and their errors, and list open questions in global QCD fitting. Finally, we anticipate how future facilities, with fixed-target and collider experiments, may impact our knowledge of PDFs and reduce their uncertainties.

Figures (14)

• Figure 1: Uncertainty bands for the $xu$ (red), $xd$ (blue), $x(\bar{d}+\bar{u})$ (green), $x(\bar{d}-\bar{u})$ (violet), $xs$ (orange) and $xg$ (black) PDFs for the CJ12mid fit CJ12 at $Q^2=10$ GeV$^2$, shown on logarithmic (left) and linear (right) scales in $x$. Note that in the left panel the gluon is scaled by a factor 1/10.
• Figure 2: Comparison of nonsinglet PDF combinations, including the valence $xu_v$ and $xd_v$, and the $x(\bar{d}-\bar{u})$ and $x(s-\bar{s})$ sea distributions, for the available 3-flavor NNLO PDF sets from JR09 JimenezDelgado:2009tv (red solid line), MSTW08 Martin:2009iq (blue dashed) and ABM11 Alekhin:2012ig (green dotted), at $Q^2=10$ GeV$^2$.
• Figure 3: As in Fig. \ref{['fig:NSpdf']}, but for the singlet-sector distributions $x(u+\bar{u})$, $x(d+\bar{d})$ and $x(s+\bar{s})$ and the gluon $xg$ PDF.
• Figure 4: $u$ and $d$ quark distributions from the CJ12mid PDFs CJ12, with PDF errors only (solid, red shaded) with combined PDF and nuclear uncertainties (dashed, blue shaded), and with a fit excluding all deuterium data (dot-dashed, green shaded), relative to the reference CJ12mid set at an arbitrary scale $Q^2=100$ GeV$^2$. Note the different vertical scales for the $u$ and $d$ quark PDFs.
• Figure 5: $d/u$ ratio for the (left) CJ12min (dot-dashed), CJ12mid (solid) and CJ12max (dashed) PDFs CJ12, and (right) CJ12mid (solid) compared with the CT10 Lai:2010vv (dot-dashed), MSTW08 Martin:2009iq (dashed) and ABKM09 Alekhin:2009ni (dot-dot-dashed) parametrizations at $Q^2=100$ GeV$^2$.