Polarized parton distribution functions in the nucleon

Polarized parton distribution functions are determined by using world data from the longitudinally polarized deep inelastic scattering experiments. A new parametrization of the parton distribution functions is adopted by taking into account the positivity and the counting rule. From the fit to the asymmetry data ${A}_{1},$ the polarized distribution functions of u and d valence quarks, sea quarks, and gluons are obtained. The results indicate that the quark spin content is $\ensuremath{\Delta}\ensuremath{\Sigma}=0.20$ and 0.05 in the leading order (LO) and the next-to-leading-order (NLO) $\overline{\mathrm{MS}}$ scheme, respectively. However, if the x dependence of the sea-quark distribution is fixed at small x by ``perturbative QCD'' and Regge theory, it becomes $\ensuremath{\Delta}\ensuremath{\Sigma}=0.24--0.28$ in the NLO. The small-$x$ behavior cannot be uniquely determined by the existing data, which indicates the importance of future experiments. From our analysis, we propose one set of LO distributions and two sets of NLO ones as the longitudinally polarized parton distribution functions.