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There are 3 types of diagrams that can contribute to a two-to-two process; the $s$-channel, $u$-channel and $t$-channel. How do I know what diagrams can contribute to a process?

I know that in QED, only $\gamma \rightarrow f\bar{f}$ vertices are allowed, where $\gamma$ is a photon, $f$ is a fermion and $\bar{f}$ is the anti-fermion.

So for the process $e^+e^- \rightarrow \mu^+ \mu^-$, only the $s$-channel is allowed and not the $t$- or $u$-channels.

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  • $\begingroup$ Read Peskin chapters 3,4,5 $\endgroup$ – InertialObserver Jan 16 at 10:42
  • $\begingroup$ All diagrams contribute to a process, upto an imposed cutoff. $\endgroup$ – Mozibur Ullah Jan 16 at 19:59
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The diagrams contributing to a process are all connected, amputated diagrams with the desired external particles that are consistent with the Feynman rules.

In a tree-level 2-2 process in a theory with only trivalent vertices, as you correctly noted, the only possible diagrams are the s, t and u - channel >-< - shaped diagrams. That is, diagrams containing 2 vertices connected by a photon.

For the process $e^{+}e^{-} \to \mu^{+}\mu^{-}$ the Feynman rules eliminate all but the s-channel diagram, because the rest contain a $\gamma \mu^{\pm} e^{\mp}$ vertex, and that doesn't exist in the theory.

If instead we considered $e^{+}e^{-} \to e^{+}e^{-}$ then only the u-channel would be eliminated since it requires a vertex $\gamma e^{\pm} e^{\pm}$.

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