Question

That's a basic thing, but, surprisingly, it is very difficult to find concise explanation of:

What is the definition of jet multiplicity?
Why is it interesting?

Answer 1

Jet multiplicity , jets in general, came to the forefront with the parton model, advocated by Feynman way before QCD was established as the theory of strong interactions.

It was experimentally observed that colliding particles formed two jets, i.e. the particles in the debris of the interaction formed two jets. The parton model, modeled them as the parton that was incoming, and had a leading effect, most of the energy, and the parton at rest which had low energy . In the center of mass system they showed the two body reaction.

Back in 1977 John Ellis et al, analysing the phenomenology of QCD proposed the mercedes diagram, where one could see in the center of mass system three jets, the two interacting partons plus a gluon.

The model is that the hard scattering of the quarks may involve a hard gluon and each of these partons is dressed by soft gluons as it materializes. High pt 3jet events clinched the existence of gluons and made the simple parton model history.

So each high pt jet is a materialization of either a primary quark or a gluon, so the multiplicity of jets has to do with QCD predictions.