Positivity of NLO Spin-Dependent Parton Distributions

We discuss the positivity of the hadron density matrix in QCD. This basic property is shown to be preserved by QCD evolution, provided the relation $\mathrm{\mid }\mathrm{\Delta }{P}_{ij}(z)\mathrm{\mid }\le P_{ij}$ is valid for all kernels for $z<1$, and the usual “+” prescription is used. We comment on the positivity restrictions for the choice of the NLO factorization scheme for the evolution of the spin-dependent parton distributions.