Many extension of the standard model contain an extra U(1) gauge group with a heavy Z gauge boson. Perhaps the most clear signal for such a Z would be a resonance in the invariant mass spectrum of the lepton pairs to which it decays. In the absence of such a signal, experiments can set limits on the couplings of such a Z, using a standard formula from theory. We repeat its derivation and find that, unfortunately, the standard formula in the literature is a factor of 8 too small. We briefly explore the implication for existing experimental searches and encourage the high energy physics community to re-examine analyses that have used this formula.
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