Determination of gluon polarization from deep inelastic scattering and   collider data
  We investigate impact of $\pi^0$-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 $\pi^0$-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 $\pi^0$ data seem to favor the node type for $\Delta g(x)$, it is difficult to determine a precise functional form from the current data. However, it is interesting to find that the gluon distribution $\Delta g(x)$ is positive at large $x$ ($>0.2$) due to constraints from the scaling violation in $g_1$ and RHIC $\pi^0$ 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 $\pi^0$-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. 
M. Hirai and S. Kumano, Asymmetry Analysis Collaboration