The process

Two beams collide head-on: electrons coming one way, positrons the other. Most of the time nothing much happens — but once in a while a collision produces something new, a muon and an antimuon, heavier carbon copies of the electron pair. This is $e^+e^- \to \mu^+\mu^-$, and it is the first process where we will compute a number: the cross section $\sigma$, the effective target area that says how often a collision makes a muon pair.

Everything is set in the center-of-momentum frame. The electron and positron arrive with equal and opposite momenta along the beam axis, and together they carry a total energy $\sqrt{s}$ — the collider's dial, and the one number that will set the scale of the answer.

The plan is the whole pipeline in one lesson. Draw the single diagram QED allows; let the Feynman rules assemble the amplitude; square it; average over the spins we don't control and sum over the ones we don't measure; integrate over every direction the muons can fly; divide by the incoming flux. What comes out the far end is $\sigma(\sqrt{s})$.