The process

In lesson 2.1 an electron and a positron met, annihilated into a single photon, and that photon produced a muon pair. This time nothing annihilates. An electron and a muon pass by each other and swap a photon: $e^-\mu^- \to e^-\mu^-$. Two particles in, the same two out — elastic scattering.

It looks like a fresh calculation. New incoming state, new outgoing state, and a photon that is now handed sideways from the electron to the muon instead of being made and destroyed. But we will not square a single new trace. The amplitude we need is the one we already have, read in a different corner of its natural variables. That move has a name: crossing.

We pick $e^-\mu^-$ on purpose — an electron and a muon are different particles, so there is exactly one diagram and none of the identical-particle bookkeeping that waits in the next two lessons. Start where every calculation on these rails starts: draw the diagram.