Determination of polarized parton distribution functions and their uncertainties

We investigate polarized parton distribution functions (PDFs) and their uncertainties by using world data on the spin asymmetry A₁. The uncertainties of polarized PDFs are estimated by the Hessian method. The up and down valence-quark distributions are determined well. However, the antiquark distributions have large uncertainties at this stage, and it is particularly difficult to fix the gluon distribution. The χ² analysis produces a positively polarized gluon distribution, but even Δg(x)=0 could be allowed according to our uncertainty estimation. In comparison with the previous Asymmetry Analysis Collaboration parametrization, accurate SLAC-E155 proton data are added to the analysis. We find that the E155 data improve the determination of polarized PDFs, especially the polarized antiquark distributions. In addition, gluon-distribution uncertainties are reduced due to the correlation with the antiquark distributions. We also show the global analysis results with the condition Δg(x)=0 at the initial scale, Q²=1 GeV², for clarifying the error correlation effects with the gluon distribution.