Comment on $Z^{\mathrm{\prime }}$'s and the H1 and ZEUS High $Q^2$ Anomalies

We investigate the effects of extra neutral gauge bosons on the high $Q^2$ region of the $e^{+}p\to e^{+}X$ cross section at $\sqrt{s}=300$ GeV. We found that the only models with electroweak strength coupling, typical of extended gauge theories, that give a better fit to the H1 and ZEUS high $Q^2$ data than the standard model, are ruled out by existing data from the Tevatron. From general scaling arguments, using the allowed contact interactions, the only allowed models with $Z^{\mathrm{\prime }}$'s would be those with strong couplings although even in this case the statistical evidence is not compelling.