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 ${A}_{1}.$ 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 ${\ensuremath{\chi}}^{2}$ analysis produces a positively polarized gluon distribution, but even $\ensuremath{\Delta}g(x)=0$ 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 $\ensuremath{\Delta}g(x)=0$ at the initial scale, ${Q}^{2}=1{\mathrm{GeV}}^{2},$ for clarifying the error correlation effects with the gluon distribution.