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I'm a relative beginner in particle physics, and the phenomenon of hadronic jets is not taught very well in my course. My understanding is that when quarks are produced in the centre of mass frame they will of course move away from each other to conserve zero momentum, but no quark can exist in isolation and the two are bound together by the attractive strong force.

However, at high enough energies the two quarks can move far enough apart that the energy from their interaction is high enough to produce an additional quark for each original quark, thus producing two bound colourless states moving in approximately the original quark directions. These, and other hadrons produced by a repeat of the same process, are what are then observed as "hadronic jets".

If this is the case, then what do we mean when we talk about interactions such as $e^+e^-\rightarrow q\bar{q}$? Do we mean that these are the quarks produced before the hadron jets form, or that there is not enough energy for hadron jets to form and so $q\bar{q}$ is the final end state and is a bound, colourless meson?

In general, just looking at a Wikipedia page on the decays of a certain meson (for example, the article on the kaon here), one will find a list of common hadronic decays, with end states listed as a small number of mesons. Are these the pions that will then separate and produce jets of hadrons? Or is my understanding flawed, and hadronic jets are not always present when quarks are produced at high enough energy?

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One should have clear in mind what are the elementary particle interactions that the experiment studies, and what are the experimental observations that lead to the accumulation of data for the study.

Here is a picture of the CMS detector at LHC

cms

It shows four outgoing particles, how they are observed/measured/defined by their trace in the various detectors.

One is interested in the crossection of the little tiny point in the center, by accumulating a large number of same type of measurements.

When the energy of the incoming target particles is small, one easily sees individual particles in the detectors , as with your question of meson decays. All outgoing are single tracks , for example the charged pion in the picture.

Jets in general are a great accumulation from the central region of a lot of tracks as the ones shown, where a number of them are bunched, rending a classical jet of particles.

An extreme number of such jets in this event, is recorded with the detector above:

cms jets

This image shows a high-multiplicity collision event observed by the CMS detector in the search for microscopic black holes, in collision data recorded in 2015. The event contains 12 jets with transverse momenta greater than 50 GeV each, and the mass of this system is 6.4 TeV. The scalar sum of the transverse energies of all energetic objects in the event (including missing transverse energy) is 5.4 TeV.

So the energy in each jet is enormous, and the number of particles in each is large, and generally jets are attributed to quarks or gluons assuming most or the energy was carried off from the original interaction by one of these non free particles/quarks. The study of the jet particle contents is important, if there are leptons in it, if particular mesons can be defined, the jet is characterized accordingly in the analysis.

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