# What is compositeness at energy scale $\Lambda$?

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 $\Lambda$.

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.
• @Matt Yes, a nonzero size of $\hbar c / \Lambda$. – knzhou Sep 11 '18 at 17:54