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Comment on $Z'$'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 $Z'$'s would be those with strong couplings although even in this case the statistical evidence is not compelling.