Is there anything smaller than quarks?

[Sen Turner]

Do we actually know for sure that quarks and leptons are as small as it gets, the complete fundamental particles? If so, how?

 

[Orodruin]

You can never know something fundamental "for sure". You can make a model and test it to the best of your abilities.

 

[mfb]

No. But we have very good indications that they are probably elementary.

(a) The energy scale. Particle accelerators can produce and study particles if their energy is sufficient. We could produce electrons and positrons as soon as the accelerators reached a few MeV (center of mass energy), we could study nuclear reactions at 10 MeV and more, we started seeing the substructure of protons at a few hundred MeV, the energy scale of the strong interaction and roughly the proton mass. Now we have 13 million MeV, and no substructure of quarks has been visible yet. If quarks are composite particles, what is the mass of their components? If they are light, we should have produced them by now. If they are heavy, how do they combine to a quark that is very light (few MeV)?
It is not impossible to write down a theory of composite quarks that is consistent with their non-observation so far, but it is very challenging and it needs very obscure assumptions. For leptons the problem is similar.

(b) Precision experiments. The most notable one is the g-factor, the ratio of the magnetic moment from spin compared to the magnetic moment from the particle motion (simplified description): For an elementary electron, the predicted value is 2.002 319 304 362 (where the last digit is uncertain). For a composite particle, the value can be everything, it can even be negative. The experimental result? 2.002 319 304 361 (where the last digit is certain). Experiment and predictions for an elementary particle agree with a precision of one part in a trillion. There is no reason why a composite particle should have a value that is even remotely similar.
Precision tests with quarks are challenging as they don't exist as isolated particles or decay too fast for better measurements, but so far everything agrees with the expectations for elementary particles as well.

While we can never be sure, composite leptons or quarks would be very odd.