Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements

Abstract

We present a new global determination of the helicity-dependent parton distribution functions (PDFs) of the proton, based on inclusive deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data within a consistent next-to-leading order (NLO) QCD framework. In addition to existing measurements, we incorporate simulated pseudodata for the future Electron-Ion Collider (EIC), considering two beam-energy configurations, $E_e \times E_p = 5 \times 41~\mathrm{GeV^2}$ and $18 \times 275~\mathrm{GeV^2}$, corresponding to an extended kinematic reach down to $x \sim 10^{-5}$. We focus on longitudinal double-spin asymmetries $A_1^h$ for charge-separated pion and kaon production in SIDIS off a longitudinally polarized proton target. These projected measurements significantly improve the flavor separation of sea-quark polarized PDFs ($Δ\bar{u}$, $Δ\bar{d}$, $Δs$) and reduce the uncertainties on both quark and gluon helicity distributions, with the largest impact at small $x$. Polarized PDFs are extracted using a neural-network parametrization and a Monte Carlo replica methodology to propagate experimental uncertainties, while theoretical constraints such as positivity are imposed during the fit. We demonstrate that the inclusion of EIC pseudodata leads to a substantially more precise determination of polarized PDFs, with the largest impact in the small-$x$ region. The resulting polarized PDF sets are provided in the {\tt LHAPDF} format.

Figures (10)

• Figure 1: Kinematic coverage in the $(x,Q^{2})$ plane for the datasets included in this analysis: polarized inclusive DIS (triangles) and polarized SIDIS $\pi^+$, $\pi^-$, $K^+$ and $K^-$ from HERMES and COMPASS (squares), together with projected EIC SIDIS asymmetries for $\pi^+$, $\pi^-$, $K^+$ and $K^-$ at $5\times41~\mathrm{GeV^2}$ (circles) and $18\times275~\mathrm{GeV^2}$ (stars). The shaded region corresponds to the excluded domain imposed by the cuts $Q^{2} > 1~\mathrm{GeV}^{2}$ and $W^{2} > 4~\mathrm{GeV}^{2}$; the horizontal line indicates the $Q^{2}$ threshold, and the curved line indicates the $W^{2}$ boundary.
• Figure 2: Impact of different $z$-cut thresholds on the quality of the global fit. The left (right) panel shows the $\chi^2$ values for the total dataset and its individual components, polarized DIS (pDIS), SIDIS, and EIC pseudodata, as a function of the minimum $z$ cut, separately for the $5\times41~\mathrm{GeV^2}$ and ($18\times275~\mathrm{GeV^2}$) configurations.
• Figure 3: Comparison of $\chi^2$ contributions for the fitted data subsets in the pDIS+SIDIS base fit (blue) and in the EIC-augmented fits (red), shown separately for the $5 \times 41~\mathrm{GeV^2}$ (upper) and $18 \times 275~\mathrm{GeV^2}$ (lower) EIC configurations. Results are displayed for the default $z_{\min}>0.2$ selection.
• Figure 4: Comparison of polarized PDFs at $Q = 10~\mathrm{GeV}$ obtained with EIC pseudodata at $5\times41~\mathrm{GeV^2}$ using two minimum-$z$ selections, $z_{\min}>0.1$ and $z_{\min}>0.2$.
• Figure 5: Comparison of polarized PDFs at $Q = 10~\mathrm{GeV}$ obtained with EIC pseudodata at $18\times275~\mathrm{GeV^2}$ using two minimum-$z$ selections, $z_{\min}>0.1$ and $z_{\min}>0.2$.