The number a detector reports

Every lesson in Part 2 has ended the same way: a curve. $\sigma(\sqrt{s})$ against energy, $\mathrm{d}\sigma/\mathrm{d}\Omega$ against angle, a marker you can slide along it and read a number off.

No experiment has ever measured that curve.

What a detector produces is a count — a number of events, an integer, with nothing continuous about it. The four LEP experiments between them recorded 15.5 million hadronic $Z$ decays and 1.7 million lepton pairs ¹. Those are the measurements. Everything else is inference.

So there is a step this course has been quietly skipping, and it is the step that connects the theory to the world. The experiments write it down explicitly:

Read left to right, that is how a measurement becomes a cross section: count what you selected, subtract what you expect from background, divide by how efficiently you were watching and by how many chances you had.

This lesson reads it right to left. Given a $\sigma$ that Part 2 taught you to compute, what integer should a detector see? Answering that needs three things we have never named: why $\sigma$ has units of area at all, what $\mathcal{L}$ is, and why $\epsilon_{\text{sel}}$ is part of the definition of the quantity rather than a correction to it.