  We show that the negative polarized gluon distribution $\Delta g$ found in a
recent global next-to-leading order QCD analysis of the nucleon helicity
structure is incompatible with the fundamental requirement that physical
cross-sections must not be negative. Specifically, we show that the fact that
this polarized gluon strongly violates the positivity condition $|\Delta g|\leq
g$ in terms of the unpolarized gluon distribution $g$ leads to negative
cross-sections for Higgs boson production at RHIC as a physical process,
implying that this negative $\Delta g$ is unphysical.
