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Suppose the quark and lepton fields weren't the fundamental fields of Nature, but that a "deeper" Lagrangian connected to a generic model of sub-quarks and -leptons would take over the conventional ones at a certain energy (in other words, the current Lagrangians connected with the quark and lepton fields are approximations). And also suppose we had enough energy available in some super high energy collider (or maybe in the LHC).

What events taking place in this collider (or maybe the LHC, as said) would (could) convince us that the quark and lepton fields are not the fundamental fields existing in Nature? With the current energies used in the LHC (the most powerful in the world, but correct me if I'm wrong) we can only conclude the quark and lepton fields are the basic fields (they are probed to distances of about $10^{-17}(m)$), but what if they are not?

The energies at which the eventual non-basal character of the quark and lepton fields would show up does, of course, vary with the model, but that would be no obstacle since we have enough energy at our disposal.

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It depends on which particles you are colliding and at which energy. When colliding a fundamental particle (or, fundamental-like at the energy scale of your experiment) with a composite particle, you would observe deep inelastic scattering between the two. This has various consequences, probably the most important being Bjorken scaling (or an analogous in this context).

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