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I am a high school student taking a modern physics course. I am reading the 1983 journal article New Tests for Quark and Lepton Substructure which covers some science and mathematics behind quark and lepton composition (theoretical). It says:

If quarks and leptons are composite at energy scale $\Lambda$, the strong forces binding their constituents induce flavor-diagonal contact interactions, which have significant effects at reaction energies well below $\Lambda$.

I want to know what the article means when it refers to compositeness at energy scale $\Lambda$.

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Fundamental particles are pointlike, with no dimensions. A composite particle made up of fundamental particles instead has a nonzero size; for example, the radius of a hydrogen atom is about $10^{-10}$ meters. And the energy $\Lambda$ just corresponds to the size $L = \hbar c / \Lambda$.

These sizes are usually quoted in terms of energies, because by dimensional analysis, we expect that relativistic quantum objects of length $L$ will have typical energies of order $\Lambda$. So the two notions are interchangeable, but energy is typically more convenient because it tells us whether our particle collider has enough energy to see the compositeness.

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  • $\begingroup$ Thank you for getting back to me so quickly! When the journal says 'If quarks and leptons are composite at energy scale Λ," is it essentially saying 'if quarks and leptons have non-zero size,"? $\endgroup$
    – Descartes Before the Horse
    Commented Sep 11, 2018 at 17:47
  • $\begingroup$ @Matt Yes, a nonzero size of $\hbar c / \Lambda$. $\endgroup$
    – knzhou
    Commented Sep 11, 2018 at 17:54

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