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I'm not certain that this question will make sense, but here goes...

In most monte carlo generators, when Z events are produced, there is a lower mass cutoff on the Z pole. I've been told that this is because the interference term with the photon would otherwise cause a divergence if you have $\gamma \to ee$ with low invariant mass.

Can anybody explain the meaning of this statement?

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It is certainly the case that there is an interference term; $G^0$ and some other projects have measured it. –  dmckee Oct 1 '12 at 14:34

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