Global QCD analysis of spin PDFs in the proton with high-$x$ and lattice constraints

TL;DR

This work delivers a comprehensive global QCD analysis of spin-dependent proton PDFs (JAMpol25) by simultaneously fitting polarized/unpolarized PDFs, fragmentation functions, and lattice observables across inclusive DIS, SIDIS, and polarized hadron-collision data, augmented by high-$x$ Jefferson Lab measurements and pseudo-Ioffe time lattice inputs. It demonstrates that including target-mass corrections and higher-twist terms, along with lattice constraints, yields stable extractions up to $x\sim 0.7$ and significantly reduces uncertainties in the valence and gluon helicity distributions, especially $ abla g$, while confirming a positive gluon polarization. The study shows that the combination of diverse observables is essential to constrain the spin structure of the proton model-independently, test sum rules such as Bjorken, and probe the low- and high-$x$ behavior; it also establishes that NNLO effects are small for current data and outlines future improvements with forthcoming facilities. Overall, the analysis provides refined, cross-validated helicity PDFs with quantified uncertainties, enabling more reliable predictions for spin-dependent processes in high-energy physics.

Abstract

We perform a comprehensive global QCD analysis of spin-dependent parton distribution functions (PDFs), combining all available data on inclusive and semi-inclusive deep-inelastic scattering (DIS), as well as inclusive weak boson and jet production in polarized $pp$ collisions, simultaneously extracting spin-averaged PDFs and fragmentation functions. Including recent Jefferson Lab DIS data at high $x$, together with subleading power corrections to the leading twist framework, allows us to verify the stability of the PDFs for $W^2 \geq 4$ GeV$^2$ and quantify the uncertainties on the spin structure functions more reliably. We explore the use of new lattice QCD data on gluonic pseudo Ioffe-time distributions, which, together with jet production and high-$x$ DIS data, improve the constraints on the polarized gluon PDF. The expanded kinematic reach afforded by the data into the high-$x$ region allows us to refine the bounds on higher twist contributions to the spin structure functions, and test the validity of the Bjorken sum rule.

Figures (23)

• Figure 1: Kinematics of polarized datasets included in this analysis with scale $Q^2$ displayed versus the relevant scaling variable. (Top panel) For polarized DIS and SIDIS the four-momentum transfer squared $Q^2$ is shown versus the Bjorken scaling variable; for jet production the transverse momentum squared is shown versus the Feynman variable; and for vector boson production the mass squared of the boson is versus $x_F$. For DIS, cuts on $W^2 > 4$ GeV$^2$ (dashed line) and $W^2 > 10$ GeV$^2$ (dot-dashed line) are also shown for reference. (Bottom panel) The scale $Q^2$ is shown versus the fragmentation variable $z = P \cdot p_h\!~/~\!P \cdot q$ for polarized SIDIS, and versus $z = 2 \, p_h \cdot q/Q^2$ for inclusive annihilation of $e^+ e^-$ pairs into $\pi$, $K$ and unidentified hadrons $h$.
• Figure 2: Stability of various truncated moments, evaluated from $x = 0.005$ to 0.52, with respect to the cut used for the polarized inclusive DIS data, for $W_{\rm min}^2 = 3.5$, 4, 5, 6 and 10 GeV$^2$, at $Q^2 = 10$ GeV$^2$: (top row) lowest moments of PDFs $\Delta u^+$, $\Delta d^+$, and $\Delta g$; (bottom row) isovector and isoscalar combinations of $\Delta u^+$ and $\Delta d^+$. The minimum value of $x$ is chosen to match the lower limit of the experimental data, while the maximum value is set by $x_{\rm max} = Q^2/(W^2 + Q^2 - M^2) = 0.52$ for $W^2 = 10$ GeV$^2$. Note that some of the points have been offset for clarity.
• Figure 3: Polarized PDFs $x \Delta f$ versus $x$ for various parton flavors $\Delta f = \Delta u$, $\Delta d$, $\Delta \bar{u}$, $\Delta \bar{d}$, along with the isosinglet $\Delta u^+ + \Delta d^+$ and nonsinglet $\Delta\bar{u} - \Delta\bar{d}$ combinations, and $\Delta g$, at $Q^2 = 10$ GeV$^2$. The JAMpol25 results with the $W^2 > 4$ GeV$^2$ cut on the inclusive polarized DIS data (red bands) are compared with those with the more restrictive $W^2 > 10$ GeV$^2$ cut (yellow bands), and those at LT (black hatched bands). Kinematically the $W^2 > 10$ GeV$^2$ cut constrains the PDFs up to $x = 0.52$ (rightmost edge of the yellow bands), while the $W^2 > 4$ GeV$^2$ cut allows PDFs to be constrained up to $x = 0.845$.
• Figure 4: Polarized to unpolarized PDF ratios $\Delta u/u$ and $\Delta d/d$ versus $x$ at $Q^2 = 10$ GeV$^2$, comparing the results with cuts $W^2 > 4$ GeV$^2$ (red bands) and $W^2 > 10$ GeV$^2$ (yellow bands) on the inclusive polarized DIS data, and the fit with $W^2 > 4$ GeV$^2$ at LT (black hatched bands).
• Figure 5: Helicity-depdendent PDFs $x\Delta f$ (for $\Delta f = \Delta u^+$, $\Delta d^+$, $\Delta\bar{u}$, $\Delta\bar{d}$, $\Delta g$) from the current JAMpol25 analysis (red bands) compared with the previous JAM17 helicity PDF fit Ethier:2017zbq (green hatched bands) and parametrizations from NNPDFpol2.0 Cruz-Martinez:2025ahf (yellow bands) and DSSV14 deFlorian:2014yva (magenta bands) at a common scale $Q^2 = 10$ GeV$^2$.