Higgs production at RHIC and the positivity of the gluon helicity distribution

We show that the negative polarized gluon distribution Δg 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 |Δg|≤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 Δg is unphysical.