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This is probably a very basic question, but I've been going through all my course materials and looking through various books to find a simple way of figuring this out. But consider the following process: $e^- e^+ \rightarrow \mu^- \mu^+$. Why is the s-channel diagram the only one that contributes to the Matrix element (only considering 2 vertices)? I could imagine writing a u channel diagram with propagator momentum p_a (initial electron) - k_2 (final antimuon). Any help is much appreciated.

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If there were a $t$-channel or $u$-channel diagram for this process, it would have to involve a vertex where an electron changes into a muon and some other particle. There is no such vertex in the standard model.

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In QED there are vertex only with the same two lepton line and one photon line. I mean that there is not vertex when $\mu\to e\gamma$ in QED.

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