Determination of gluon polarization from deep inelastic scattering and collider data

TL;DR

The paper addresses how to determine gluon polarization Δg(x) within nucleons by performing a global analysis that combines polarized deep inelastic scattering data, RHIC π^0 production data, and projected JLab E07-011 g1^d measurements. It employs NLO DGLAP evolution, a Hessian uncertainty framework, and tests two Δg shapes (positive and node-type) to assess the robustness of the gluon extraction. Key findings include a substantial reduction of Δg(x) uncertainty from RHIC π^0 data, a potential node-type Δg(x) near x ~ 0.1, and a further significant improvement from precise JLab E07-011 data via both antiquark–gluon correlations and explicit NLO gluonic contributions in g1^d, leading to notable reductions in the gluon first moment ΔG for x>0.1. The work highlights the complementary roles of collider and DIS data in constraining polarized parton distributions and provides a public AAC08 polarized PDF library for broader use.

Abstract

We investigate impact of $π^0$-production data at Relativistic Heavy Ion Collider (RHIC) and future E07-011 experiment for the structure function $g_1$ of the deuteron at the Thomas Jefferson National Accelerator Facility (JLab) on studies of nucleonic spin structure, especially on the polarized gluon distribution function. By global analyses of polarized lepton-nucleon scattering and the $π^0$-production data, polarized parton distribution functions are determined and their uncertainties are estimated by the Hessian method. Two types of the gluon distribution function are investigated. One is a positive distribution and the other is a node-type distribution which changes sign at $x \sim 0.1$. Although the RHIC $π^0$ data seem to favor the node type for $Δg(x)$, it is difficult to determine a precise functional form from the current data. However, it is interesting to find that the gluon distribution $Δg(x)$ is positive at large $x$ ($>0.2$) due to constraints from the scaling violation in $g_1$ and RHIC $π^0$ data. The JLab-E07-011 measurements for $g_1^d$ should be also able to reduce the gluon uncertainty, and the reduction is comparable to the one by RUN-5 $π^0$-production data at RHIC. The reduction is caused by the error correlation between polarized antiquark and gluon distributions and by a next-to-leading-order (NLO) gluonic effect in the structure function $g_1^d$. We find that the JLab-E07-011 data are accurate enough to probe the NLO gluonic term in $g_1$. Both RHIC and JLab data contribute to better determination of the polarized gluon distribution in addition to improvement on polarized quark and antiquark distributions.

Figures (9)

• Figure 1: Kinematical region of the DIS data is shown by $x$ and $Q^2$. The notations $p$, $n$, and $d$ indicate proton, neutron, and deuteron, respectively.
• Figure 2: Comparison of the polarized PDFs between the analyses A and B. They are shown by the dashed and solid curves for the analyses A and B, respectively, at $Q^2$=1 GeV$^2$. Their uncertainties are shown by the shaded bands.
• Figure 3: Polarized antiquark and gluon distributions by the analysis B which includes the RHIC $\pi^0$-production data. The distributions and their uncertainties are calculated at $Q^2=1$ GeV$^2$. Positive and node-type solutions are shown by the solid and dashed-dot curves, respectively.
• Figure 4: Comparison of the polarized PDFs between the current analysis B and AAC06 for the positive $\Delta g(x)$. They are shown by the dashed and solid curves for the AAC06 and the current analysis (AAC08), respectively, at $Q^2$=1 GeV$^2$. Their uncertainties are shown by the shaded bands.
• Figure 5: Set-B results are compared with the PHENIX data in the longitudinal double spin asymmetry of $\vec{p} +\vec{p} \rightarrow \pi^0 +X$phenix-pi. The solid curves and the shaded bands indicate theoretical asymmetries and their uncertainties by the HKNS07 fragmentation functions. The results by the KKP and Kretzer fragmentation functions are shown by the dashed and dashed-dot curves, respectively.