Polarized Gluon Distribution Functions in Leading Order and Next-to-Leading Order

Quark and gluon contributions to the nucleon spin are described by polarized parton distribution functions (polarized PDF) and their first moments. It became clear that only a small fraction of nucleon spin is carried by quarks and antiquarks. Therefore, a large gluon polarization or effect of orbital angular momenta should be possible sources for explaining the origin of the nucleon spin. Polarized PDFs have been investigated by global analyses of data on polarized lepton - nucleon DIS and proton - proton collisions [1, 2, 3, 4, 5-12]. Polarized quark distributions are determined relatively well, however the polarized gluon distribution is not accurately determined. The gluon distribution contributes to the structure function g1 as a higher order effect in the expansion by the running coupling constant of QCD.