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

We show that the negative polarized gluon distribution $\mathrm{\Delta }g$ 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 $\mathrm{\mid }\mathrm{\Delta }g\mathrm{\mid }\le g$ 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 $\mathrm{\Delta }g$ is unphysical.